UC-NRLF 


SB    272    243 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

Class 


REINFORCED 
CONCRETE 

A  MANUAL  OF  PRACTICE 


NET  BOOK -This  Book  is  sup- 
plied to  the  trade  on  terms  which  do 
not  admit  of  discount. 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 


v  (cr\os  i  i 

OF 


CHICAGO  AND  NEW  YORK 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 
1008 


REINFORCED 
CONCRETE 

A  MANUAL  OF  PRACTICE 


BY 
ERNEST  McCULLOUGH 

Af.  W.  S.  £.,  Author  of  "Engineering  Work  in  Towns  and 
"  Th*  B usiness  of  Contracting ."  '  'Engineering  Contractors 
Posktt  Book,"  Etc.,  Etc.          </ 

l 


OF  THE     "         ^t 

UNIVERSITY   I 

OF 


CHICAGO  AND  NEW  YORK 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 
1008 


t  I 


1 


Copyright  1908 

By 
THE  MYRON  C.  CLARK  PUBLISHING  Co. 


NOTES    AND    CORRECTIONS. 

The  formulas  given  in  the  first  twenty-two  pages  are  those  devel- 
oped by  Professor  Talbot,  and  credit  is  given  on  page  17.  The  same 
formulas  are  found  in  Turneaure  &  Maurer's  "Principles  of  Reinforced 
Concrete  Construction . ' ' 

Page  13.  The  definition  of  the  modulus  of  elasticity  given  on  this 
page  is  to  be  found  in  Trautwine's  Civil  Engineers  Pocket  Book,  which 
has  been  a  standard  since  1876.  The  description  on  this  page  of  how 
the  modulus  is  obtained  is  to  be  found  in  all  the  standard  works  on 
mechanics  of  materials. 

Page  22.     Seventh  line  from  the  top.     Formula  should  read — 
M=fpd'bd2         or         M=fpd'dbd         or         M=/Ad'd 

Page  59.  Twenty-third  line  from  top.  "The  maximum  stress  is 
0.853h,"  should  read  "the  maximum  stress  is  0.583h,"  etc. 

Page  60.  Top  and  second  line  should  read  "and  D  =  internal 
diameter  in  feet." 

On  the  same  page  near  the  bottom,  the  two-thirds  rule  for  pressure 
on  footings  applies  only  to  rectangular  surfaces  and  not  to  circular.  It  is 
customary  to  construct  rectangular  footings  for  chimneys. 

Page  107.  Seven  lines  from  bottom.  The  acid  bond  solution  is 
generally  composed  of  ninety  parts  water  and  ten  parts  chemically  pure 
hydrochloric  acid,  although  some  men  use  stronger  solutions. 

Pages  31  and  98.  The  custom  of  stopping  work  in  the  middle  of 
slabs  and  in  midspan  of  beams  instead  of  at  the  supports  is  spreading  and 
results  obtained  seem  to  justify  it.  The  joint  is  made  where  there  is  the 
least  amount  of  steel  and  where  consequently  stops  can  be  readily  placed. 
Care  should  be  taken  to  secure  a  good  junction  of  new  work  to  old  when 
resuming  work.  This  method  does  away  with  practically  all  the  objec- 
tions to  T  beams. 

August  15,  1908. 

Reinforced  Concrete;   A  Manual  of  Practice.     McCullough. 


173474 


To 

W.  A.  STEVENSON,  ESQ., 

of  the 

NORWOOD  ENGINEERING  CO., 

This  Book  is  respectfully 

DEDICATED. 


173474 


PREFACE. 

This  book  is  intended  to  be  what  its  title  indicates,  A 
Manual  of  Practice.  The  intention  in  the  sections  on  design 
has  been  to  keep  within  the  usual  requirements  of  the  ordinary 
conservative  building  ordinances  of  American  cities.  This 
explains  the  use  of  the  straight  line  formulas  for  stress  and  the 
limitations  imposed  by  the  employment  of  working  stresses. 
The  ambitious  designer  wishing  to  learn  more  of  the  theory 
of  the  subject  and  the  design  of  higher  structures  can  go  to  the 
larger  standard  treatises  and  have  nothing  to  unlearn. 

So  far  as  construction  is  concerned,  the  principles  stated 
herein  as  the  result  of  personal  experience,  apply  to  all  manner 
of  work  in  reinforced  concrete,  and  to  this  extent  the  book 
should  be  of  some  value  to  a  large  number  of  men.  Good  work- 
manship implies  no  knowledge  of,  or  dependence  upon,  theory 
of  design.  It  simply  calls  for  the  exercise  of  common  sense, 
unremitting  vigilance  and  care  on  the  part  of  the  man  in  charge, 
a  willingness  to  learn  from  every  intelligent  workman  on  the 
job,  and  the  kind  of  pride  that  takes  honestly  to  heart  the  les 
sons  of  experience.  The  motto,  if  the  manager  is  the  sort  of 
man  who  believes  in  mottoes,  is  Do  not  forget! 

If  the  manager,  however,  does  not  know  something  about  the 
theory  of  design,  then  the  owner  is  taking  great  chances.  The  man 
in  charge  should  be  an  engineer. 

The  writer  feels  the  preface  would  be  incomplete  unless 
he  acknowledged  here  the  assistance  given  him  by  his  son 
George  Seymour  McCullough  in  checking  and  recalculating  the 
tables,  many  of  them  original.  The  work  was  at  times  irksome, 
and  we  trust  no  errors  will  be  discovered. 

Some  assistance  received  from  readers  who  followed  the 
articles  as  they  appeared  in  The  Cement  Era  has  been  acknowl- 
edged in  the  proper  places  in  preparing  the  articles  for  pub- 
lication in  book  form. 

Errors  and  omissions  discovered  and  reported  by  readers 
will  be  gratefully  acknowledged,  and  whatever  the  readers  may 
do  to  assist  in  making  future  editions  mor/-  valuable  will  be 
appreciated. 

E.  McC. 

Chicago,  111.,  U.  S.  A.,  May,  1908. 


CONTENTS. 

CHAPTER  I. — STRENGTH  OF  BEAMS 9 

Simple,  Practical  Formulas — Neutral  Axis — Modulus  of  Elasticity — 
Tables  of  Factors — Elastic  Limit — Per  Cent  of  Steel — Design  of  a 
Beam — Strength  of  Concrete  of  Stone  and  Cinders — Fibre  Stresses — 
Empirical  Formulas — Beam  Failures — Web  Stresses — Stirrups — Weights 
and  Areas  of  Steel — Double  Reinforced  Beams — T  Beams — Allowable 
Stresses  in  Building  Ordinances — Adhesion  of  Concrete — Floor  Slabs — 
Continuous  Beams. 

CHAPTER  II. — LOADS  ON  BEAMS 35 

Reactions — Bending  Moments — Deflection — Shear — Concentrated  Loads 
— Distributed  Loads — Combinations  of  Loads — Parallel  Forces  on  Beams 
— Freely  Supported  Beams — Tied  Beams — Cantilever  Beams — Dead  Load 
— Live  Loads — Methods  for  Assuming  Beam  and  Slab  Calculations — 
Load  Permitted  by  Building  Ordinances — Highway  Bridges — Sidewalks. 

CHAPTER  III. — COLUMNS 44 

Comparison  of  Sizes  in  Different  Materials — Methods  of  Reinforcing 
Columns — Ratio  of  Length  to  Thickness — Area — Tables  of  Column 
Divisors — Different  Formulas  for  Strength  and  Stiffness — Increase  of 
Strength  with  Added  Steel — Comparison  of  Steel  and  of  Steel  and 
Concrete — Safe  Fibre  Stresses — Methods  of  Working — Pouring  Columns 
— Foundations — Footings — Placing  Vertical  Steel. 

CHAPTER  IV.— WALLS,  TANKS  AND  FOOTINGS 52 

Plain  vs.  Reinforced  Walls — Calculation  of  Pressu're — Unit  Pressures 
Surcharged  Walls— Detailed  Calculations  for  Wall— Restrained  Walls- 
Circular  Tanks — Design  of  Chimney — Footings. 

CHAPTER  V. — DESIGN  AND  COST 64 

Examination  of  Reasons  for  Reinforced  Concrete  Construction — Ad- 
hesion— Shrinkage  of  Concrete — Connections — Use  of  Wire — Holes  in 
Slabs — Comparison  with  Wood — Remarks  on  Cost  and  on  Conduct  of 
Work — Different  Methods  of  Design — Forms — An  Approximate  Method 
of  Estimating  Costs. 

CHAPTER  VI.— FORMS 75 

General  Remarks  from  Practical  Experience — Studded  Frame  Forms — 
Ransome  Panels — Framed  Panels — Board  by  Board  Methods — Wiring — 
Bracing — Bolts  and  Ties — Spacers — Corner  Forms — Beam  and  Slab 
Forms — Column  Forms — Hints  on  Form  Design  and  Estimating. 

CHAPTER  VII.— THE  CONDUCT  OF  WORK 93 

Unit  of  Measurement — Table  of  Mixtures — Hand  Mixing — Machine 
Mixing — Measuring  Aggregates — Wheelbarrows — Quantity  of  Water — 
Filling  Forms — Finishing  Surfaces — Dense  Concrete — Tools  for  Good 
Work — Importance  of  Placing  Steel — Pouring  Concrete — Tables  of 
Pressure  of  Concrete — Spacing  of  Wire  and  Bolts — Safe  Loads  on 


Posts  and  Braces— Weights  of  Nails,  Spikes  and  Bolts— Strength  of 
Beams — Oiling  Forms — Soap — Wetting  Forms — Compressed  Air — Steam 
for  Cleaning— Joining  New  Work  to  Old— Perfect  Joints— To  Prevent 
Freezing — Protecting  Work. 

CHAPTER  VIIL— TOOLS Ill 

Ordering  Steel — Shears  and  Punches — Keeping  Track  of  Steel — Forges 
—Benders  for  Steel— Cold  Chisels— Cold  Cutters— Snips— Pliers— Bars 
—Hammers — House  Raising  Jacks — Blocks  and  Tackles — Saws — Nail 
Pullers — Concrete  Boxes  and  Doors — Hoists — Electricity — Gasoline 
Engines — Air  Compressors — Steam — Pipe  Coverings — Wheelbarrows — 
Concrete  Carts — Dumping  Buckets — Conveyor  Systems — Sub-letting 
Work. 


CHAPTER  I. 
STRENGTH  OF  BEAMS. 

Formulas  for  reinforced  concrete  design  are  in  reality  very 
simple  and  can  be  used  by  any  practical  man.  The  majority  of 
writers  on  the  subject,  however,  write  for  men  who  retain  a  knowl- 
edge of  the  mathematics  of  college  days  and  give  the  derivation  of 
the  formulas.  Men  who  have  forgotten  their  higher  mathematics 
and  men  who  have  not  gone  to  college  look  for  something  short 
and  easy  and  use  empirical  formulas  and  easy  rules  rather  than 
wade  through  pages  of  mathematical  reasoning  to  finally  reach 

M  =  K  bd1 

which  is  the  formula  wanted  and  which  is  not  recognized  when 
reached. 

It  means  that  the  resisting  moment  of  the  beam  is  equal  to 
K  (a  moment  factor),  multiplied  by  the  breadth  of  the  beam 
times  the  square  of  the  depth. 

Nothing  can  be  more  simple,  and  when  tables  containing  values 
of  "K"  are  available  the  application  is  easy. 

To  obtain  the  size  of  a  beam  change  the  formula  to  read: 


in  which  M=bending  moment=resisting  moment  in  inch  pounds. 

d=depth  in  inches  from  top  of  beam  to  center  of  steel  rein- 
forcement. 

b=breadth  in  inches. 

The  moment,  M,  is  found  when  we  know  the  clear  span  and 
load.  The  breadth,  b,  we  can  generally  assume  at  1/20  to  1/24 
the  span,  and  K  is  taken  from  tables. 

Remember  that  in  the  following  pages  the  depth  of  the  beam  is 
always  the  distance  from  the  top  to  the  center  of  the  steel  rein- 
forcement. The  concrete  below  the  steel  is  simply  there  for  pro- 
tection and  is  not  relied  upon  to  add  strength  to  the  beam. 

Assume  the  breadth,  b,  at  from  1/20  to  1/24  the  span,  for 
the  reason  that  the  upper  part  of  the  beam  is  a  column  and  to 
prevent  side  bending,  or  undue  stresses  at  its  junction  with  the 


10  Reinforced  Concrete. 

slab  on  top,  the  length  should  not  exceed  24  times  the  least 
thickness.  Therefore  assume  a  breadth  as  above  and  solve  for 
d.  The  best  shaped  beam  is  one  in  which  b  lies  between  J^d 
and  ^d.  To  obtain  such  a  beam  may  require  two  or  more 
trials,  until  designing  experience  has  been  gained. 

There  must  be  enough  concrete  surrounding  the  steel  to 
permit  of  a  good  grip.  Practice  has  shown  that  this  should  be 
not  less  than  1  inch ;  and  when  the  bars  are  more  than  Y%  of 
an  inch  in  diameter  or  thickness,  this  covering  should  be  not 
less  than  one  and  one-half  such  thickness  or  diameter. 

When  several  bars  are  used  the  space  between  them  should 
be  at  least  twice  their  thickness  or  diameter.  If  the  beam  is  too 
narrow  to  permit  of  this  they  should  then  be  in  two  planes,  stag- 
gered. Rods  or  bars  should  be  of  such  a  size  that  their  length 
will  exceed  50  times  their  thickness.  On  this  point  we  will  speak 
later. 

Grip  is  not  alone  to  be  considered.  Where  danger  from  fire  is 
to  be  feared  then  the  least  covering  should  be  2  inches.  Experi- 
ments have  proven  that  the  adhesion  between  steel  and  concrete 
is  impaired  by  continuous  submersion,  so  walls  designed  to  hold 
water  should  have  a  covering  of  not  less  than  2  inches  over  the 
steel,  and  should  be  made  of  very  dense  concrete. 

At  this  point  the  writer  believes  it  will  be  well  to  give  a  few 
reasons.  Few  men  are  satisfied  with  a  rule  until  they  know  why 
it  exists  in  the  particular  form  given.  In  this  respect  all  writers 
agree,  but  in  the  present  instance  the  formula  is  given  first  and  the 
reasons  follow.  The  practical  man  wants  to  know  the  meaning  of 
the  terms  "Neutral  ^..xis,"  "Elastic  Limit"  and  "Modulus  of  Elas- 
ticity" and  why  the  theorist  makes  use  of  them. 

Neutral  Axis. 

The  position  of  the  neutral  axis  in  a  rectangular  beam  de- 
pends upon  the  material  of  which  the  beam  is  made.  Wood, 
wrought  iron  and  steel  being  practically  as  strong  in  compres- 
sion as  in  tension  are  made  into  beams  of  such  shape  that  the 
neutral  axis  is  in  the  middle.  Cast  iron  being  about  four 
times  as  strong  in  compression  as  in  tension  is  made  into  beams 
shaped  like  a  letter  T  upside  down.  The  neutral  axis  is  at  a 
point  which  divides  the  area  of  the  beam  so  that  the  area  in 
compression  is  equal  to  one-fourth  of  the  area  in  tension. 

Concrete  is  about  ten  times  as  strong  in  compression  as 
in  tension,  but  is  so  much  weaker  than  cast  iron  that  it  cannot 


Neutral  Axis.  11 

be  fashioned  the  same.  So  it  is  cast  into  rectangular  beams  and 
steel  bars  are  placed  in  the  bottom  to  take  care  of  the  tension. 

The  exact  location  of  the  neutral  axis  is  very  important  in 
the  design  of  reinforced  concrete  beams  and  slabs ;  but  the  undue 
prominence  given  this  point  has  been  the  cause  of  much  bad 
work,  for  when  touching  upon  this  point  exact  writers  soar  into 
realms  of  mathematics  where  most  men  cannot  follow.  Believing  in 
a  dim  way  that  all  the  x's,  y's  and  z's  are  a  part  of  the  rules,  men 
with  practical  rather  than  theoretical  training  use  rules  given  in 
manufacturers'  catalogues  or  picked  up  loosely  from  any  source, 
caring  nothing  for  the  derivation,  provided  they  look  easy. 

When  a  beam  bends,  the  fibres  in  the  lower  part,  below  the 
neutral  axis,  stretch.  Above  the  neutral  axis  the  fibres  are  com- 
pressed. The  neutral  axis  therefore  lies  in  a  plane  in  which  the 
longitudinal  fibres  undergo  no  change. 

k-  Compression—:  — > 


t  \       /\ 

1    '-    /     \   /' 

-v---:/-----.-^-^^ 

*'  ^'s- 

I  /  \  /  \ 

i^~  -~        * 

*   '   .      ,     x.'              ^ 

;< Tens/on > 

FIG.  1 — DIAGRAM  OF  TENSION  AND  COMPRESSION. 

Figure  1.  The  stretching  force  exerted  at  the  bottom 
may  be  plotted  as  a  horizontal  line.  Erect  a  perpendicular 
from  the  middle  of  the  line,  the  height  being  equal  to  the  depth 
of  the  beam.  Connect  the  ends  of  all  the  lines  and  we  have  a 
triangle,  the  apex  being  at  the  top  of  the  beam  and  the  base 
being  at  the  bottom.  Through  the  apex  draw  another  horizontal 
line,  the  length  being  equal  by  scale  to  the  compressive  force. 
Connect  the  ends  to  the  middle  of  the  base  of  the  first  triangle 
and  we  have  a  second  triangle  superimposed  on  the  first.  A 
perpendicular  connecting  the  middle  points  in  the  base  of  each 
triangle,  the  side  lines  of  each  cross  at  a  point  proportional  to 
the  length  of  the  bases.  The  neutral  axis  passes  through  the 
points  where  the  side-lines  cross. 

The  stress  is  proportional  to  the  distance  from  the  netural 
axis  but  we  can  see  by  the  above  description  that  the  neutral 


Reinforced  Concrete. 


axis  is  not  like  a  fulcrum,  but  is  located  where  opposing  forces 
balance.  All  this  preliminary  explanation  is  necessary  in  order 
to  show  how  "K"  is  obtained,  that  we  may  use  the  moment  fac- 
tor intelligently. 

To  some  men  educated  in  the  mechanics  of  materials, 
Fig.  1  looks  strange,  so  Fig.  3  will  be  more  acceptable  to  them. 

When  a  beam  bends  the  assumption  is  made  that  a  section 
plane  before  bending  remains  plane  after  bending;  that  is,  a 
section  of  the  beam  such  as  would  be  made  by  a  vertical  saw 
cut.  In  Fig.  3  the  section  before  bending  is  represented  by  the 
vertical  line  and  the  differences  betwen  its  position  and  that  of 
the  inclined  line  represent  the  tensile  and  compressive  stresses 
in  the  beam. 

Representing  the  extreme  fibre  stress  in  the  concrete  by  c, 
and  the  steel  fibre  stress  by  f,  we  have 

fp  =  y2ck 

which  will  be  explained  in  the  next  section. 


I, 


T 


It  is  -assumed  that  all  tension  is  carried  by  the  steel  and 
that  the  unit  deformation  in  any  horizontal  fibre  varies  directly 
as  its  distance  from  the  neutral  axis. 

To  illustrate  this  graphically  look  again  at  the  two  force 
triangles.  Erase  all  the  lines  except  the  top  one  representing 
compression  and  the  lower  one  representing  tension.  Join  the 
opposite  ends  so  there  will  be  two  small  triangles  with  the 
apices  at  the  neutral  axis.  Forces  act  through  the  center  of 
gravity  of  bodies  and  the  center  of  gravity  of  a  triangle  is  one- 
third  the  distance  from  the  base. 


Modulus  of  Elasticity.  13 

This  explains  -y,  which  indicates  the  position  of  the  point 
where  the  compressive  strength  of  the  concrete  is  concentrated. 

Modulus  of  Elasticity. 

This  is  a  force  which,  if  such  a  thing  were  possible,  would 
stretch  a  material  to  twice  its  original  length  or  compress  it 
one-half.  It  is  generally  designated  by  the  capital  letter,  E.  In 
reinforced  concrete  work  Es  is  the  designation  for  this  force 

TT« 

in  steel,  and  EC  for  concrete.  The  ratio  -£-  is  n.  To  deter- 
mine the  modulus  of  elasticity  of  a  material,  stretch  or  com- 
press a  piece  of  unit  size,  some  definite  amount  by  means  of 
some  definite  force.  Multiply  the  original  length  by  this  force. 
Divide  the  product  by  the  area  of  cross-section  multiplied  by 
the  amount  of  compression  or  stretch.  The  result  is  E. 

E  for  steel  is  taken  at  from  29,000,000  pounds  to  31,000,000. 
A  value  of  30,000,000  is  commonly  used.  As  the  values  are  aver- 
ages the  difference  between  the  E  of  high  carbon  and  medium 
steel  is  not  worth  considering. 

E  for  concrete  varies  with  the  mixture,  the  age  and  the  care 
with  which  the  concrete  is  mixed.  It  is  not  uniform  throughout 
a  piece  of  concrete. 

It  is  usual  in  building  ordinances  to  specify  "n,"  and  the 
ratios  most  in  use  are  8,  10,  12,  15  and  20. 

Take  beams  of  some  unit  width  and  some  unit  depth.  Rein- 
force each  with  some  percentage  of  steel  and  apply  a  certain 
load  to  each  beam.  Assuming  some  ratio  of  extensibility  be- 
tween the  two  materials  we  find  that  the  position  of  the  neutral 
axis  varies  with  the  percentage  of  steel  and  the  ratio  assumed 
between  the  moduli  of  elasticity. 

Table  I  has  been  calculated  by  such  a  method.  The  values 
of  "n"  are  shown  at  the  tops  of  the  columns.  The  letter  "p" 
stands  for  percentage  of  steel,  being  the  area  of  the  steel  di- 
vided by  the  product  of  the  depth  and  breadth  of  the  beam,  the 
depth  being  distance  from  center  of  steel  to  top  of  beam. 

The  decimals  give  the  values  of  "k"  and  show  the  distance 
from  the  top  of  the  beam  to  the  neutral  axis,  expressed  in  per- 
centage of  total  depth,  "d."  The  formula  is: 


=  y( 


2P-  n  +  p?  n8     —  p.  n 


14 


Reinforced  Concrete. 


The    values    of   "k"   thus    obtained,    are    used    to    calculate 
"K"  in  Table  III.     It  is  usual  to  assume  some  definite  value  in 

TABLE  I.    Values  of  k. 


Area 
of 
steel 
=P 

Es 

TT=n 

8 

10 

12 

15 

20 

.005 
.006 
.007 
.008 
.009 
.01 
.0125 
.015 

.25 
.27 
.28 
.30 
.31 
.33 
.36 
.38 

.27 
.29 
.31 
.33 
.34 
.36 
.39 
.42 

.29 
.31 
.33 
.35 
.37 
.38 
.42 
.45 

.32 
.34 
.36 
.38 
.40 
.42 
.45, 
.48  / 

.35 
.38 
.41 
.43 
.45 
.46 
.50 
.53 

compression  for  concrete  and  some  definite  tensile  stress  for 
steel,  and  by  so  doing  we  can  obtain  values  of  "k"  by  this 
formula. 


Where  k  =  percentage  of  depth  of  neutral  axis  below  top  of 
beam. 

p=percentage  of  steel. 

f=fibre  stress  in  steel  per  square  inch. 

c=extreme  compressive  stress  in  concrete. 

Table  II  has  been  computed  by  means  of  the  above  formula, 
using  values  of  "f"  and  "c"  in  common  use. 

The  Chicago  building  ordinance  will  not  permit  a  value  of 
"c"  exceeding  500  pounds  per  square  inch.  The  value  of  "f" 
may  be  one-third  the  elastic  limit.  The  value  of  "n"  is  fixed  at 
12.  What  steel  can  we  use? 

In  Table  I  look  under  12  for  values  of  "k."  In  Table  II 
we  next  look  under  500  to  get  the  same  values,  and  find  we 
can  use  from  .7  to  1.0  per  cent  of  steel  stressed  10,000  pounds 
per  square  inch,  from  0.6  to  0.9  of  steel  stressed  12,500  pounds, 
from  0.5  to  0.7  of  steel  stressed  15,000  pounds,  or  16,000  pounds, 
0.5  to  0.6  of  steel  stressed  18,000  pounds,  or  0.5  of  steel  stressed 
20,000  pounds.  Of  course  for  the  stronger  steel  much  smaller 
percentages  might  be  used  but  less  than  0.5  of  steel  makes  an 
expensive  beam,  which  remark  will  be  better  understood  after 
learning  how  to  use  Table  III.  When  a  small  percentage  of  steel 
is  used  the  size  of  the  beam  is  increased. 


Design  of  Beams. 


15 


Looking  in  column  500  in  Table  III  we  obtain  a  moment 
factor  "K"  opposite  the  values  of  "k"  taken  from  Table  I  and 
by  the  formula 

d  = 


Kb 

the  size  of  the  beam  may  be  computed.     Narrow,  deep  beams 
are  cheaper  and  stiffer  than  wide  and  shallow  beams. 

Beams  should  be  limited  if  possible  in  width  as  already 
explained  and  the  depth  should  not  exceed  1/10  the  span.  When 
impossible  to  keep  within  the  limits  set,  the  internal  stresses 
require  careful  investigation  and  provision  must  be  made  to 
take  care  of  them. 

TABLE  II.    Values  of  k. 


4 

f=  10000 

f=12500 

f=15000 

Area 
of 

Values  of  c. 

Values  of  c. 

Values  of  c. 

steel 

=P 

500 

600 

700 

800 

500 

600 

700 

800 

500 

600 

700 

800 

.005 

.20 

.17 

.14 

.13 

.25 

.21 

.18 

.16 

.30 

.25 

.21 

.19 

.006 

.24 

20 

.17 

.15 

.30 

.25 

.21 

.19 

.36 

.30 

.26 

.23 

.007 

.28 

.23 

.20 

.18 

.35 

.29 

.25 

.22 

.42 

.35 

.30 

.26 

.008 

.32 

.27 

.23 

.20 

.40 

.33 

.29 

.25 

.48 

.40 

.34 

.30 

.009 

.36 

.30 

.26 

.23 

.46 

.38 

.33 

.29 

.54 

.45 

.39 

.34 

.01 

.40 

.33 

.29 

.25 

.50 

.42 

.36 

.31 

.60 

.50 

.43 

.38 

.0125 

.50 

.42 

.36 

.31 

.63 

.52 

.45 

.39 

.75 

.63 

.54 

.47 

.015 

.60 

.50 

.43 

.38 

.75 

.63 

.54 

.47 

.90 

.75 

.64 

.56 

A  r~n 

f  =16000 

f=18000 

f=^20000 

Area 
of 

Values  of  c. 

Values  of  c. 

Values  of  c. 

steel 

=P 

500 

600 

700 

800 

500 

600 

700 

800 

500 

600 

700 

800 

.005 

.32 

.27 

.23 

.20 

.36 

.30 

.26 

.23 

.40 

.33 

.29 

.25 

.006 

.38 

.32 

.27 

.24 

.43 

.36 

.31 

.27 

.4'8 

.40 

.34 

.30 

.007 

.45 

.37 

.32 

.28 

.51 

.42 

.36 

.32 

.56 

.47 

.40 

.35 

.008 

.51 

.43 

.37 

.32 

.58 

.48 

.41 

.36 

.64 

.53 

.46 

.40 

.009 

.58 

.48 

.41 

.36 

.65 

.54 

.46 

.41 

.72 

.60 

.52 

.45 

.01 

.64 

.53 

.46 

.40 

.72 

.60 

.52 

.45 

.80 

.67 

.57 

.50 

.0125 

.80 

.67 

.57 

.50 

.90 

.75 

.64 

.56 

X 

.84 

.72 

.63 

.015 

.96 

.80 

.69 

.60 

X 

.90 

.77 

.68 

X 

X 

.86 

.75 

In  Table  III,  "k"  is  the  distance  from  top  of  beam  to  the 
neutral  axis,  -g-  is  the  distance  down  to  the  center  of  gravity 
of  the  compression  triangle,  d'  is  the  moment  arm  or  distance 


16 


Reinforced  Concrete. 


from  the  steel  to  the  point  -g-      The  moment  factors  K,  in  the 

columns   headed   500,   600,    700    and  800    are  obtained  by  the 
formula 

K=Hcd'k, 
where  c=fibre  stress  in  most  remote  fibre  of  concrete. 

d'=moment  arm. 

k=depth  of  neutral  axis. 

TABLE  III.    Values  of  Moment  Factor  K. 


k 

y& 

d' 

500 

Value 
600 

5  of  c. 
700 

800 

.25 

.083 

.917 

57.3 

68.8 

80.2 

91.7 

.27 

.09 

.91 

61.5 

73.7 

86.0 

98.3 

.28 

.093 

.907 

63.5 

76.1 

88.8 

101.5 

.29 

.097 

.903 

65.5 

78.5 

91.6 

104.8 

.30 

.10 

.90 

67.5 

81.0 

94.5 

108.0 

.31 

.103 

.897 

69.5 

83.4 

87.3 

110.1 

.32 

.107 

.893 

71.5 

85.7 

100.0 

114.1 

.33 

.11 

.89 

73.4 

88.1 

102.8 

117.5 

.34 

.113 

.887 

75.3 

90.5 

105.3 

120.5 

.35 

.117 

.883 

77.3 

92.7 

108.0 

123.5 

.36 

.12 

.88 

79.2 

95.0 

110.9 

126.8 

.37 

.123 

.877 

81.0 

97.2 

113.4 

129.7 

.38 

.127 

.873 

83.0 

99.5 

116.0 

132.7 

.39 

.13 

.87 

84.8 

101.8 

118.8 

135.8 

.40 

.133 

.867 

86.7 

104.0 

121.4 

138.8 

.41 

.137 

.863 

88.5 

106.0 

123.9 

141.5 

.42 

.14 

.86 

90.3 

108.3 

126.3 

144.4 

.43 

.143 

.857 

92.0 

110.5 

129.0 

147.4 

.45 

.15 

.85 

95.6 

114.8 

134.0 

153.0 

.46 

.153 

.847 

97.4 

116.8 

136.2 

155.8 

.48 

.16 

.84 

100.8 

120.9 

141.0 

161.0 

.50 

.167 

.833 

104.0 

125.0 

143.8 

166.6 

.53 

.177 

.823 

109.0 

130.9 

152.8 

174.5 

Sometimes  a  wall  or  partition  of  concrete  can  be  reinforced 
with  steel  and  thus  be  strengthened  to  carry  certain  loads  and  re- 
lieve the  footings.  As  the  breadth  and  depth  are  fixed,  assuming 
a  certain  percentage  of  steel,  p,  a  stress,  c,  in  the  concrete  and  a 
depth,  k,  of  the  neutral  axis,  the  fibre  stress,  f,  of  the  steel  is  ob- 
tained by  the  formula 

f  =  #  c  k 

P 

With  the  explanations  given  there  should  be  no  trouble  in 
selecting  a  moment  factor,  K,  when  given  p,  c,  f  and  n  or  when 
given  two  of  them  with  the  others  assumed. 


Elastic  Limit.  17 

The  theory  on  which  the  above  treatment  is  based  is  deduced 
from  experiments  made  at  the  University  of  Illinois,  Engineering 
Experiment  Station,  under  the  direction  of  Prof.  Arthur  N.  Talbot, 
but  regards  only  what  is  called  the  straight  line  distribution 
of  stresses  for  working  loads.  For  ultimate  loads  the  para- 
bolic distribution  of  stresses  is  used. 

Elastic  Limit. 

Nearly  all  materials  have  a  certain  amount  of  elasticity  and 
will  resume  their  original  shape  and  size  after  being  stressed. 
There  is  a  point,  however,  beyond  which  they  cannot  be  stressed 
without  permanent  distortion  and  this  point  is  called  the  elastic 
limit.  In  steel  it  is  from  five  to  six-tenths  the  ultimate  strength. 

After  steel  has  been  stressed  past  its  elastic  limit  it  stretches 
faster  under  load  and  the  cross-section,  of  course,  is  reduced. 
If  imbedded  in  concrete,  the  adhesion  is  destroyed  and  as  the 
steel  stretches,  more  load  is  thrown  on  the  concrete.  Conse- 
quently the  strength  of  the  beam  depends  upon  the  elastic  limit 
of  the  steel  and  the  ultimate  strength  of  the  concrete,  for  con- 
crete can  hardly  be  said  to  have  an  elastic  limit. 

Up  to  within  a  year  or  two  the  claim  was  made  that  when 
steel  having  a  high  elastic  limit  was  used,  a  considerable  saving 
could  be  effected.  If  it  took  one  per  cent  of  steel  having  an 
elastic  limit  of  36,000  pounds  per  square  inch  then  it  would  take 
only  about  six-tenths  per  cent  of  steel  having  an  elastic  limit  of 
64,000  pounds  per  square  inch. 

This  is  true,  however,  only  when  the  question  of  deflection 
is  not  considered,  but  not  true  if  it  is.  We  have  seen  that  the 
relative  extensibility  of  steel  and  concrete  must  govern  and 
that  the  E  of  high  carbon  and  medium  steel  differ  slightly, 
although  one  may  have  double  the  strength  and  nearly  double 
the  elastic  limit  of  the  other. 

The  steel  stretches  per  unit  of  length  as  indicated  by  the 
division  of  the  fibre  stress  in  pounds  per  square  inch  by  the 
modulus  of  elasticity. 

The  Ransome,  Thacher,  Kahn  and  Johnson  bars  made  of 
medium  steel  have  the  elastic  limit  raised  and  the  ultimate 
strength  increased,  by  the  processes  to  which  they  are  subjected 
in  preparing  them  for  market.  The  drawing  of  wire  has  the 
same  effect,  in  a  greater  degree,  on  the  metal  of  which  it  is 
made. 

Medium  steel  has  been  found  more  reliable  in  general  struc- 


18  Reinforced  Concrete. 

tural  work  than  high  carbon  steel,  and  it  is  to  be  supposed,  is 
therefore  best  for  reinforced  concrete  work.  As  the  ultimate 
strength  of  a  reinforced  concrete  beam  depends  upon  the  elastic 
limit  and  not  upon  the  ultimate  strength  of  the  steel,  for  eco- 
nomical design,  where  not  restricted  by  conservative  building 
ordinances,  a  high  elastic  limit  is  desirable.  This  is  furnished 
by  the  numerous  deformed  bars  of  medium  steel  and  also  by 
plain  and  twisted  bars  of  high  carbon  steel  made  from  old  rails. 
For  situations  where  shocks  may  be  experienced,  as  in 
water  pipes,  floors,  floor  beams,  arches,  etc.,  medium  steel  should 
be  used  and  if  high  stresses  are  permitted  in  the  concrete,  the 
bars  should  be  deformed.  In  retaining  walls,  tank  walls,  sewers, 
etc.,  high  carbon  steel  may  be  used.  »As  a  rule  the  twisted,  high 
carbon  steel  now  advertised  by  many  firms,  will  cost  as  much 
per  pound  as  plain  bars  of  medium  steel  and  be  much  cheaper 
than  deformed  bars  of  medium  steel.  It  can  be  usually  shipped 
more  promptly. 

Per  Cent  of  Steel 

Reinforced  concrete  design  has  not  yet  reached  the  point 
where  formulas  can  be  used  without  judgment.  Seven-tenths 
per  cent  of  steel,  as  compared  with  one  per  cent,  does  not  al- 
ways mean  just  what  it  seems. 

Take  for  example,  a  beam  to  resist  a  bending  moment  of 
100,000-inch  pounds.  We  know  that  n=12,  so  in  Table  I.  we  find 
under  12  that  k=.33  when  0.7  per  cent  of  steel  is  used,  and  k=.38 
when  1.0  per  cent  of  steel  is  used. 

It  is  assumed  that  the  concrete  cannot  be  stressed  more 
than  500  pounds  per  square  inch,  so  in  Table  II.  we  find  in  the 
column  headed  500,  that  opposite  0.007  the  fibre  stress  in  the 
steel  is  about  12,000  pounds,  corresponding  to  an  elastic  limit  of 
36,000  pounds,  if  we  are  held  to  one-third  the  elastic  limit.  One 
per  cent  of  steel  means  a  little  less  than  10,000  pounds  or  prac- 
tically an  elastic  limit  of  30,000  pounds. 

We  look  next  in  Table  III  under  column  headed  500,  and 
opposite  k=.33,  we  find  K=73.4  and  the  moment  arm  is  89%  of 
d.  Opposite  k=r.38,  we  find  K=83.0  and  the  moment  arm  is 
87.3%  of  d. 

Assume  a  width  of  8  inches  and  our  first  beam  is  as  follows: 


d  _  J  IPO  OOP   =   1305,, 

V   73.4  V  8 


73.4  X  8 
Allowing  for  concrete  to  cover  the  steel,  call  the  total  depth  15 


Factor  of  Safety.  19 

inches.  13.05x8=104.4"x.007=.73  square  inches  of  steel.  The 
nearest  to  this  will  be  three  ^"  square  bars,  weighing  .85X3—2.55 
pounds  per  foot  of  beam.  Our  beam  8"xl5"  contains  .833  cubic 
feet  of  concrete.  At  $6.00  per  cubic  yard  this  means  22  cents 
per  cubic  foot  or  18.3  cents  per  lineal  foot.  At  2  cents  per  pound 
the  steel  will  cost  5  cents,  making  a  total  cost  for  the  beam  of 
23.3  cents  per  lineal  foot. 
The  second  beam  is 

d  _  ^  100  QUO      _    122,, 

Allowing  for  the  same  depth  of  concrete  to  cover  the  steel, 
we  get  a  beam  8x14".  It  should  really  be  14.15",  but  we  will  keep 
to  the  nearest  half  inch.  By  calculations  similar  to  those  just 
completed,  we  find  the  cost  of  this  beam  to  be  23.9  cents  per 
lineal  foot.  The  difference  is  a  trifle  less  than  three  per  cent, 
due  to  the  fact  that  the  smaller  percentage  of  steel  goes  with  a 
larger  beam. 

Factor  of  Safety. 

The  statement  that  steel  having  a  high  elastic  limit  gives  a 
better  factor  of  safety  than  steel  having  a  low  elastic  limit,  per- 
haps need  some  explanation,  since  we  have  explained  the  difference 
between  modulus  of  elasticity  and  elastic  limit. 

Turn  to  Table  I.  with  n=12  take  k=.38,  corresponding  to 
one  per  cent  of  steel.  From  Table  III  under  concrete  stressed 
500  pounds  K=83.0. 

Under  600  pounds,  K=83.4  and  k=.31. 

Under  700  pounds,  K=83.1  and  k=.26. 

As  we  have  taken  n=12,  turn  again  to  Table  I  and  opposite 
k=.31,  p=0.6%.  Opposite  k=26,  p=OA%  (about). 

This  value  of  n  limits  us  in  using  Tables  II    and  III. 

Under  f=10,000,  c=500,  km.38,  p=0.95%, 

Under  f=15,000,  c=600,  k=.3l,  p=0.62%. 

Under  f=16,000,  c=600,  k=r.31,  p=:0.58%. 

Under  f=18,000,  c— 700,  k=.26,  p=0.5%. 

Under    f=18,000,    c=700,    k=.26,   p=0.5%. 

Under    f=20,000,    c=z70Q,    k=.26,    p=0.4%. 

This  shows  how  the  different  percentages  of  steel  in  a  beam 
of  a  specified  size  alter  the  unit  stresses  in  both  concrete  and 
steel  when  a  definite  value  is  given  to  n,  the  ratio  of  extensi- 
bility. 

If  a  beam  is  designed  for  a  certain  percentage  of  steel  hav- 
ing a  low  elastic  limit  and  the  state  of  the  steel  market  and  the 


20  Reinforced  Concrete. 

time  limit  on  the  job  compel  the  use  of  high  carbon  steel,  the  use 
of  an  equal  amount  of  high  carbon  steel  insures  a  stronger 
beam. 

If  high  carbon  steel  is  used  and  the  designer  decides  to  keep 
to  the  same  factor  of  safety,  thus  using  less  of  the  high  carbon 
steel,  the  beam  will  not  be  so  stiff  as  with  the  larger  amount  of 
steel.  When  a  concrete  beam  bends  innumerable  cracks  open  in 
the  bottom.  They  may  be  microscopic,  but  if  in  depth  they  extend 
to  the  steel,  moisture  may  enter  and  corrode  it. 

Where  values  of  c,  f  and  n  are  not  fixed  by  ordinance,  the 
designer  can  exercise  his  judgment  to  secure  economy,  care 
being  taken  not  to  lean  too  far  toward  the  danger  line. 

Therefore  it  is  best  to  pay  no  attention  to  the  ultimate 
strength  of  the  steel  but  keep  within  a  factor  of  safety  of  three, 
or  one-third  the  elastic  limit. 

The  following  table  gives  the  ultimate  strength  we  should 
consider  for  different  concrete  mixtures,  and  the  safe  fibre  stress 
should  be  one-fourth  the  ultimate  strength,  to  correspond  to 
one-third  the  elastic  limit  of  the  steel.  The  values  given  are 
averages  for  concrete -30  days  old  and  good  workmanship  will 
put  the  strength  above  the  average.  Concrete  grows  stronger 
with  age  and  the  greatest  strains  come  on  beams  and  floors  gen- 
erally about  one  month  after  the  concrete  is  poured. 

ROCK    CONCRETE. 

1:2:4 2,450  pounds  per  square  inch  in  compression. 

1:2:5 2,400        "          "         "         "     " 

1:3:5 2,000 

1:3:6 1,900         "          "         "         "     "  " 

1:3:8 1,800        "          "         "         "     "  " 

1:4:8 1,500         "          "         "         "     " 

CINDER    CONCRETE. 

1     2:4 900   pounds   per   square   inch   in   compression. 

1     2  :5 700        „  „        „  „       „ 

1     3  :6 500        „  „        „  „      „ 

The  modulus  of  elasticity,  with  usual  loads,  at  end  of  30 
days  is  about  as  follows: 

ROCK    CONCRETE. 

1:2:4 2,600,000    pounds. 

1:2:5 2,450,000 

1:3:5 2,400,000 

1:3:6 2,300,000 

1:3:8 2,100,000        " 

1:4:8 2,000,000 


Simple  Formulas.  21 

Cinder  concrete  has  a  modulus  of  elasticity  of  about  1,040,- 
000  pounds. 

For  the  above  values  of  rock  concrete  n  will  be  from  12 
to  15  and  for  cinder  concrete  it  will  be  from  25  to  30.  Some 
men  use  35  to  40  for  cinder  concrete. 

Rock  concrete  weighs  from  140  to  145  pounds  per  cubic 
foot,  and  for  estimating  purposes  with  the  steel  in  it,  the  weight 
is  generally  assumed  at  from  145  to  150  pounds.  Cinder  con- 
crete is  generally  assumed  as  weighing  from  110  to  115  pounds 
per  cubic  foot  reinforced. 

The  designer  should  endeavor  to  get  just  the  right  amount 
of  steel  in  the  beam.  Too  much  steel  means  increased  expense 
and  also  danger  that  the  beam  will  be  destroyed  by  the  con- 
crete crushing  out  at  the  top.  This  does  not  give  warning 
enough.  If  the  amount  of  steel  is  small  the  beam  will  deflect 
considerably  before  the  concrete  is  over-stressed. 

The  foregoing  formulas  place  the  neutral  axis  in  the  posi- 
tion it  occupies  just  before  the  beam  fails,  when  the  steel  is 
stressed  to  the  yield  point,  the  elastic  limit.  As  the  formulas 
given  are  termed  "Straight  line"  formulas,  the  actual  position 
of  the  neutral  axis  is  a  trifle  below  this  point,  so  there  is  an 
additional  factor  of  safety  up  to  a  load  which  implies  that  the 
fibre  stresses  calculated  have  been  reached.  For  ultimate  loads 
we  must  use  formulas  based  on  the  parabolic  distribution  of 
stress,  and  such  formulas  are  not  discussed  in  this  book,  as  we 
deal  only  with  working  loads. 

The  only  drawback  to  the  straight  line  formula  in  the  opin- 
ion of  some  designers,  is  that  the  amount  of  steel  is  too  small 
for  the  ultimate  load  that  can  be  borne  by  the  concrete.  For 
the  most  economic  designing  a  knowledge  of  the  parabolic  the- 
ory is  desirable,  but  for  all  practical  work,  and  for  designing 
under  the  limitations  imposed  by  building  ordinances,  the 
straight  line  theory  is  perfectly  satisfactory. 

To  obtain  the  fibre  stresses  in  a  beam  already  designed  the 
preceding  pages  may  be  consulted.  For  the  benefit,  however, 
of  men  not  used  to  transposing  equations  the  following  formulas 
are  given.  Representing  the  moment  arm  by  d '  =  d  —  x  (ex- 
pressed as  a  decimal,  representing  a  percentage  of  d,  precisely 
as  k  is  represented  as  a  percentage  of  d),  then 


22  Reinforced  Concrete. 

T  =  total  tension  in  the  steel  in  pounds. 
C  =  total  compression  in  the  concrete  in  pounds. 
M  =  bending  moment  to  be  resisted,  in  inch  pounds. 
then 


--d'd 

The    material    deficient    in   amount    determines    the    actual 
strength  of  the  beam,  so  to  find  M  as  fixed  by  the  steel, 
M  =  fpd'dbd2 

A 

in  which  d'd  represents  the  moment  arm  in  inches,  and  p  —  -r-r 

the  percentage  of  steel,  bd  being  the  area  of  the  concrete  above 
the  center  of  the  steel. 

The  strength  of  the  beam  as  fixed  by  the  concrete  is 

M  =  y2c  k  d'd  bd2. 

T 
The  fibre  stress  in  the  steel  is  f  =  ~^~i  where  A  is  the  area 

of  the  steel  in  square  inches.     Another  formula  is  given  under 
Table  III. 

The  fibre  stress  in  the  concrete  is 

2fp 
:    k 

Other  Formulas. 

From  the  results  of  experiments  in  which  the  above  for- 
mulas have  been  demonstrated  to  be  correct,  another  set  of 
formulas  have  been  derived. 

There  are  three  stages  in  the  testing  to  destruction  of  a  re- 
inforced concrete  beam.  Until  the  steel  has  been  stressed  to 
about  one-third  the  -yield  point  the  neutral  axis  is  stationary. 
It  then  rises  until  the  steel  is  stressed  to  about  one-half  the 
yield  point,  after  which  it  remains  nearly  stationary  in  position 
until  the  beam  fails,  when  it  drops. 

Some  men  believe  it  is  perfectly  safe  to  design  for  safe 
loads  and  assume  the  neutral  axis  to  be  in  the  middle  of  the 
beam  and  ignore  the  relative  extensibilities  of  the  two  materials. 

Let  c=stress  in  extreme  horizontal  layer  of  concrete  per 
square  inch. 

f=fibre  stress  in  steel. 

b=breadth  of  beam. 

d=depth  from  top  of  beam  to  center  of  steel. 

x=concrete  modulus. 


Simple  Formulas.  23 


d'=nnoment  arm. 
p=percentage  of  steel 


~r  =  p 

M=xbdXd'd=Kbd«. 
Take  the  concrete  at  500  pounds,  then 

500  ^p  =  125  bd. 

1  pc 

Take  £=10,000  Ibs.,  then  10QOO  =0.0125=p. 

Assuming  the  neutral  axis  at  the  middle  of  the  beam  and 
the  center  of  compressive  forces  in  the  concrete  at  one-sixth  of 
the  depth  of  the  beam  we  have  f  d=0.833d=d',  the  moment  arm, 
and  125  b  dX0.833d=l04b  d'=M. 

Recognizing  that  the  modulus  of  elasticity  and  the  elastic 
limit  are  different  factors  having  different  influences  on  the 
strength  of  the  beam,  and  that  the  position  of  the  neutral  axis 
in  the  middle  of  the  beam  is  true  only  when  percentage  of  steel 
is  from  1.0  to  1.25  per  cent,  the  following  modification  has  been 
proposed  to  the  above  formula: 

This  value  of  K=104,  is  maintained  as  a  basis,  but  p  varies 

with  the  fibre  stress  in  the  steel=  -^- 

The  value  of  K  obtained  as  above,  is  maintained  for  p=1.0% 
and  over.  When  p  is  less  than  1.0%  take  0.50-f(  --  p""^/  ==d"' 

which  varies  as  may  be  seen,  with  p.    Then 

xbdXd"dXp=Kbd«. 
Example:    Use  p  =  0.8%  then 


125  bdX0.916dXo.8=91.6bd*. 

The  depth  of  the  neutral  axis  from  the  top  of  the  beam 
will  then  be  k  =  0.27  -f  0.18  p. 

By  the  above  method  tables  of  K  may  be  calculated  and 
used.  The  only  excuse  for  such  a  formula  is  that  it  is  more 
readily  remembered  than  the  more  exact  ones,  but  this  excuse 


24  Reinforced  Concrete. 

vanishes  when  it  requires  modification  to  permit  of  more  ra- 
tional designing  with  varying  percentages  of  steel. 

Such  a  formula  is  useful  at  times  when  some  piece  of  work 
is  to  be  done  and  table  books  and  abstruse  formulas  are  not  at 
hand.  The  rationale  is  simple,  hence  easily  remembered  and 
applied. 

For  all  practical  purposes  it  is  first-class  practice  to  con- 
sider the  neutral  axis  as  occupying  a  position  in  the  middle  of 
the  beam  and  use  1.25%  of  steel;  making  the  depth  of  the  beam 
from  1-10  to  1-12  the  span  and  having  the  breadth  between  Y* 
and  y$-  the  depth.  It  may  not  be  the  most  economic  beam  but 
it  will  certainly  be  safe  if  shown  to  be  able  to  resist  the  bending 
moment  caused  by  the  loading. 

Beam  Failures. 

When  a  beam  breaks  by  showing  large  cracks  near  the  mid- 
dle at  the  bottom  and  an  appearance  of  crushing  at  the  top, 
the  cause  generally  is  failure  by  tension  in  the  steel.  In  such 
a  case  not  enough  steel  is  used  for  the  quality  of  concrete  ob- 
tained. 

When  the  failure  is  by  breaking  of  the  concrete  on  top, 
then  too  much  steel  has  been  used.  The  beam  fails  by  compres- 
sion in  the  concrete. 

Beams  failing  by  showing  diagonal  cracks  at  the  bottom 
near  the  supports  fail  by  diagonal  tension  in  the  concrete. 

When  the  width  of  a  beam  is  1/20  to  1/24  the  span  and  is 
at  least  one-half  the  depth,  the  beam  will  likely  fail  by  tension 
in  the  steel  or  compression  in  the  concrete.  When  the  beam 
is  short  and  deep,  it  may  fail  by  diagonal  tension  or  the  bond 
may  be  destroyed  between  the  steel  and  concrete. 

Let  V=vertical  shear  on  the  beam. 

o=circumference  or  periphery  of  bar  in  inches. 
m=number  of  bars. 
u—  bond  per  square  inch. 
d'=moment  arm. 

then  "^ 


As  the  adhesion  is  expressed  in  pounds  per  $q.  in.  mo= 
total  surface  of  bars  per  sq.  in.  of  length. 

The  periphery  of  a  half  inch  bar  is  4  X  1A  —  2  inches  and 
the  periphery  of  a  one-inch  bar  is  4  inches.  Four  half-inch  bars 
have  the  tensile  strength  of  one  bar  one  inch  square  but  have 


Beam  Failures.  25 

4X2=8  inches  of  bond  surface,  or  double  that  of  the  one- 
inch  bar. 

Building  ordinances  generally  specify  the  bond  or  adhesion 
so  the  amount  should  be  tested  by  the  above  formula.  If  the 
amount  of  steel  has  been  found  sufficient  for  bending  moment 
but  not  sufficient  for  bond,  it  is  plain  that  smaller  bars  may  be 
used  in  order  to  get  the  increase  of  surface  necessary. 

The  stresses  tending  to  destroy  the  bond  between  the  con- 
crete and  the  steel  are  transmitted  to  the  surrounding  concrete. 
This  gives  a  horizontal  unit  shearing  stress  we  will  call  v.  In 
value  it  is  equal  to 

v=bd' 

where  b  =  breadth  of  beam.  This  v  is  also  equal  to  the  vertical 
unit  shearing  stress  at  a  point  just  above  the  level  of  the  rein- 
forcing bars. 

V 

The  formula  vb  =  -jp-  gives  the  rate  of  vertical  stress  pec 

unit  of  length  of  beam  that  will  go  into  stirrups  if  they  are 
found  necessary. 

To  illustrate:  Having  found  the  bending  moment,  calculate 
the  size  of  the  beam  and  amount  of  steel  necessary  to  resist  it. 
Next  determine  the  number  of  rods  required,  remembering  the 
space  between  the  rods  should  be  at  least  equal  to  the  thick- 
ness. Next  test  for  bond.  When  this  is  settled  test  for  the 
horizontal  and  vertical  unit  shearing  stress  and  if  it  exceeds 
the  tensile  strength  of  the  concrete,  stirrups  must  be  provided. 
Stirrups  as  a  rule  are  necessary  only  in  deep  short  beams. 

By  the  above  formula  stirrups  will  be  placed  the  entire 
length  of  the  beam.  Some  designers  use  stirrups  in  every  beam 
while  others  simply  use  them  when  the  analysis  indicates  the 
necessity  for  them.  Even  when  an  analysis  may  show  them  to 
be  really  not  necessary  it  adds  considerably  to  the  strength  of 
the  beam  to  provide  them  and  the  cost  is  not  great.  A  sheet 
of  expanded  metal  or  wire  fabric  in  the  web  of  the  beam  is 
excellent  and  performs  the  work  of  stirrups. 

Stirrups  should  be  either  fastened  to  the  bottom  steel  or 
should  be  bent  in  U  shape  with  the  bottom  rods  going  through 
this  loop.  They  may  be  inclined  at  an  angle  of  45  degrees  to- 
ward the  ends  of  the  beam,  or  they  may  be  vertical.  Inclined  stir- 
rups are  most  efficient,  but  they  are  troublesome  to  place. 


26  Reinforced  Concrete. 

An  empirical  rule  given  by  E.  L.  Ransome  for  stirrups  is 
to  place  four  at  each  end  of  the  beam,  the  first  to  be  J4  the 
depth  from  the  end,  the  second  to  be  ^2  the  depth  from  the 
first,  the  third  to  be  §4  the  depth  from  the  second,  and  the 
fourth  to-be  a  distance  equal  to  the  depth  from  the  third.  These 
stirrups  are  generally  *4  to  f^-inch  rods.  In  small  beams  they 
may  be  of  extremely  heavy  wire,  one  stirrup  hooking  around 
each  bottom  reinforcing  rod. 

All  stirrups  should  go  to  within  one  inch  of  the  top  of  the 
slab  on  the  beam  and  then  run  about  six  inches  into  the  slab. 
In  any  case  they  should  go  to  within  about  an  inch  of  the  top 
of  the  concrete  and  be  bent  to  run  parallel  with  it  for  about  six 
inches.  They  should  be  used  even  when  the  reinforcement  is 
bent  upward  toward  the  ends  of  the  beam. 

Beams  having  some  of  the  reinforcing  bars  bent  up  near 
the  ends  are  stronger  than  beams  having  all  the  bars  straight. 
This  is  because  of  better  bond,  or  is  due  to  a  change  in  di- 
rection of  the  stresses.  Each  designer  seems  to  be  at  present 
a  law  unto  himself  as  to  manner  of  bending  the  bars.  The 
writer  turns  up  one-fourth  of  the  rods  at  the  quarter  span  point, 
one-third  of  the  remainder  at  the  sixth  point  and  one-fourth  of 
the  remainder  at  the  eighth  point.  The  remainder  go  straight 
to  the  support  and  when  a  little  past  it  are  turned  straight  up 
at  least  six  inches. 

The  bent  rods  go  at  an  angle  of  45  degrees  to  within  one 
inch  of  the  top.  If  at  the  end  of  a  simple  beam  they  bend  at 
the  top  and  go  clear  over  to  the  support  and  are  anchored  by 
bending.  If  the  beam  is  continuous,  or  fastened  at  the  end  (as 
common  with  reinforced  concrete  beams),  the  bent  rods  stop 
at  the  top  of  the  beam.  In  the  top  of  the  beam  across  the 
supports  are  placed  one-half  as  many  bars  as  are  used  in  the 
bottom.  These  top  bars  go  across  to  the  quarter  span  points 
and  are  there  turned  down  at  an  angle  of  45  degrees  and  termi- 
nate one  inch  from  the  bottom. 

It  is  common  now  to  have  brackets  connecting  beams  to 
walls  and  heavy  pillow  blocks  under  beams  at  posts.  Diagonal 
tie  bars  go  through  these  projections  which  thus  act  as  braces 
and  stiffen  the  structure  in  case  of  unequal  settlement  of  founda- 
tion or  in  case  of  earthquake. 

When  bars  lap  past  each  other  they  should  lap  at  least 
twenty-five  times  the  thickness.  No  bar  should  be  of  a  size 


>>^ 

OF  THE     '         \ 

UNIVERSITY  j 

U\!       Amount  of  Reinforcement. 


that  its  length  in  a  beam  will  be  less  than  fifty  times  the  thick- 
ness or  diameter. 

When  the  reinforcing  steel  is  stressed  more  than  10,000  Ibs.  per 
sq.  in.  deformed  bars  should  be  used.  Twisted  bars  are  good  enough 
for  all  practical  purposes,  but  all  the  bars  in  the  market  are  good, 
although  extravagant  claims  are  made  for  some. 

The  important  fact  must  be  remembered  that  it  makes  no  dif- 
ference in  what  form  the  reinforcement  conies.  The  amount  to  use 
for  strength  can  be  determined  by  the  formulas  already  given  and 
no  matter  what  the  claims  of  the  advertiser  no  smaller  amounts 
can  be  used  without  lowering  the  value  of  the  factor  of  safety. 
This  remark  applies  to  the  strength  of  the  steel  to  resist  breaking. 

Deformed  bars  and  rods  increase  the  hold  of  the  concrete  and 
thus  enable  the  designer  to  utilize  more  of  the  strength  of  the  steel 
than  if  adhesion  alone  is  depended  on.  As  a  general  rule  at  present 
prices  the  most  economical  beam  contains  steel  stressed  about  16,000 
Ibs.  per  sq.  in.,  with  the  concrete  stressed  about  570  Ibs.  per  sq.  in. 
The  writer  would  not  think  it  safe  to  stress  plain  steel  to  exceed 
10,000  Ibs.  per  sq.  in.,  so  in  using  a  higher  stress  he  employs  de- 
formed bars  or  rods. 


TABLE   IV. 

Weights  per  lineal  foot  and  areas  of  square  bars  and  round 


rods. 


One  cubic  foot  of  steel  weighing  490  Ibs. 
One  cubic  inch  of  steel  weighing  0.283  Ib. 


Thickness 
or 
Diameter. 

Weight 
Ib. 
(Square.) 

Area, 
in. 
(Square.) 

Weight, 
Ib. 
(Round.) 

Area, 
in. 
(Round.) 

J4     inch 

H 
H 

% 
M 
H 
i 

.212 
.478 
.85 
1.328 
1.913 
2.603 
3.4 

.0625 
.1406 
.25 
.3906 
5625 
.7656 
1.00 

.167 
.376 
.668 
1.043 
1.502 
2.044 
2.67 

.0491 
.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

Table  IV  will  be  of  assistance  in  using  ordinary  plain  and  twist- 
ed steel.  The  manufacturers  of  special  reinforcing  material  gladly 
give  to  all  inquirers  pamphlets  and  circulars  containing  tables  of 
sizes  and  weights  of  their  materials. 

Fabrics,  whether  woven,  welded  or  expanded  from  sheets,  so 


28  Reinforced  Concrete. 

bind  the  concrete  that  the  stress  is  distributed  over  a  wider  area 
than  when  bars  are  used,  but  not  enough  to  safely  reduce  the  amount 
of  steel.  The  advantage  claimed  for  fabrics  is  that  they  should  cost 
less  to  put  in  place  than  it  costs  to  put  in  rods  or  bars  properly. 
When  beams  and  slabs  are  designed  the  steel  is  assumed  to  occupy 
a  definite  position.  To  insure  this  all  pieces  should  be  wired  at  in- 
tersections. This  costs  a  great  deal  and  the  makers  of  fabrics 
claim  that  by  the  use  of  their  material  the  cost  of  placing  steel  is 
lessened  and  the  certainty  of  getting  it  in  the  correct  position  as- 
sured. 

Double  Reinforced  Beams. 

There  is  seldom  any  occasion  to  design  a  beam  reinforced 
both  in  the  top  and  bottom,  but  occasionally  it  is  unavoidable. 
Steel  used,  however,  in  the  compression  side  of  a  beam  is  ex- 
pensive, for  it  cannot  be  stressed  as  high  as  steel  in  the  tension 
side. 

When  the  bottom  of  the  beam  is  stressed  we  know  that 
innumerable  small  cracks  open  that  can  seldom  be  detected 
even  with  a  microscope,  for  they  are  distributed  because  of  the 
adhesion  to  the  steel.  For  this  reason  we  neglect  the  tensile 
strength  of  the  concrete,  as  the  cracks  open  before  the  steel 
is  stressed  more  than  three  or  four  thousand  pounds  per  square 
inch. 

In  the  upper  part  of  the  beam  we  cannot  exceed  a  certain 
fixed  fibre  stress  in  the  concrete,  so  can  only  stress  the  steel 
in  proportion  to  the  ratio  of  the  moduli  of  elasticity  of  the  two 
materials.  Consequently  while  the  fibre  stress  in  the  tension 
steel  may  be  as  high  as  16,000  pounds  per  square  inch,  the  com- 
pression steel  cannot  be  stressed  to  exceed  6,000  to  9,000  pounds 
per  square  inch,  depending  upon  its  depth  below  the  top  of  the 
beam. 

M.  Bonna  placed  steel  in  both  sides  oi'  all  beams  he  designed 
and  his  formulas  are  as  follows: 

Let  A^area  in  square  inches  of  tension  steel. 

A'^area  in  square  inches  of  compression  steel. 
M=rbending  moment  in  inch  pounds. 

d=moment    arm   between   centers   of   steel    reinforcement 
in  bottom  and  top  of  beam. 

Then  A=^-,  and  A'  =  %  A. 

The  compressive  strength  of  the  concrete  is  depended  upon 


Double  Reinforced  Beams.  29 

for  a  certain  amount  of  resistance  and  it  is  not  necessary  to 
make  any  calculations  for  the  position  of  the  neutral  axis.  To 
the  moment  arm,  d,  it  is  simply  necessary  to  add  enough  to 
thoroughly  cover  and  protect  the  steel  in  each  side  of  the 
beam.  This  total  depth,  therefore,  will  depend  upon  the  head 
room  wanted  and  the  consequent  depth  of  beam  that  can  be 
permitted. 

The  bending  moment  being  obtained  from  the  span  and 
loading  and  f  being  assumed,  according  to  the  grade  of  steel 
used, 


Usually,  however,  the  problem  comes  to  us  in  the  form  of 
a  beam  that  has  already  been  designed  and  which  cannot  be 
enlarged  because  the  plans  have  proceeded  to  such  a  point  that 
alterations  cannot  be  made,  yet  some  new  ideas  have  arisen 
which  call  for  a  much  heavier  loading  on  the  beam.  The  only 
way  to  take  care  of  this  load  is  to  proportion  the  steel  in  the  bot- 
tom to  carry  it,  thus  increasing  the  fibre  stress  on  the  concrete. 

If  the  building  ordinance  will  not  allow  the  higher  stress 
in  the  concrete,  then  enough  steel  must  be  placed  in  the  com- 
pression side  of  the  beam  to  balance  the  additional  amount  of 
steel  in  the  tension  side,  without  changing  the  position  of  the 
neutral  axis  as  originally  designed,  and  thereby  keeping  the 
concrete  fibre  stress  down  to  where  it  was  originally  calculated. 

In  order  that  the  steel  and  the  concrete  will  deform  equally, 

f  =  nc, 
and  this  cannot  be  exceeded. 

If  this  ratio  is  used,  however,  it  would  imply  that  the  com- 
pression steel  will  be  placed  in  the  top  of  the  beam,  for  c  is  the 
extreme  fibre  stress,  decreasing  to  0  at  the  neutral  axis.  As 
the  compression  steel  will  be  placed  below  the  top  of  the  beam, 
where  the  stress  will  be  less  than  c,  and  in  amount  =r  c'  we  then 
have,  calling  the  compression  steel  stress  =  f, 
f'  =  nc'. 

The  moment  arm  of  the  beam  as  originally  designed  ex- 
tended from  the  plane  of  the  tension  steel  to  the  centroid  of 
compression  of  the  concrete.  When  the  compression  steel  is 
added  there  is  another  moment  arm  added  which  is  equal  in 
length  to  the  distance  between  the  planes  of  the  tension  and 


30  Reinforced  Concrete. 

compression  steel.     The  length  of  this  moment  arm  is  chosen 
arbitrarily. 

The  area  of  the  original  tension  steel  is  A  and  the  addi- 
tional steel  added  to  that  side  of  the  beam  we  will  call  a,  while 
the  area  of  the  compression  steel  will  be  A'.  Then  to  find  the 
area, 


That  is,  we  multiply  the  fibre  stress  in  the  tension  steel  by 
the  additional  area  of  the  tension  steel  and  divide  by  the  fibre 
stress  of  the  concrete  in  the  plane  of  the  compression  steel, 
multiplied  by  the  ratio  between  the  moduli  of  elasticity,  in 
order  to  obtain  the  area  of  the  compression  steel. 

The  area  of  the  compression  steel  being  governed  by  its 
depth  below  the  top  of  the  beam,  if  a  floor  slab  rests  on  the 
beam  and  is  to  be  poured  at  the  same  time,  a  calculation  can 
be  made  to  increase  the  depth  of  the  beam  by  considering  the 
thickness  of  the  floor  slab  as  a  part  of  it.  Placing  the  com- 
pression steel  then  in  the  floor  slab  will  result  in  some  saving 
of  steel,  by  materially  lengthening  the  moment  arm  between  the 
steel  reinforcements. 

To  prevent  any  tendency  to  buckle  on  the  part  of  the  com- 
pression steel,  small  stirrups  should  be  hung  over  it  at  inter- 
vals not  exceeding  twelve  times  the  thickness  of  the  bars  or 
rods  used,  and  these  anchoring  stirrups  should  go  clear  to  the 
bottom  steel. 

The  internal  stresses  in  the  beam  should  be  carefully  com- 
puted when  double  reinforcement  is  used  and  it  may  be  found 
advisable  to  make  the  reinforcement  in  the  top  and  bottom  of 
angle  iron  connected  by  a  sheet  of  expanded  metal,  or  of  rods 
fastened  together  by  expanded  metal  or  wire  fabric,  thus  mak- 
ing the  beam  practically  a  plate  girder. 

T  Beams. 

Some  designers  have  a  great  fondness  for  designing  what 
are  known  as  T  beams,  in  which  the  floor  slab  above  the  beam 
is  intended  to  carry  all  compression  and  the  beam  consequently 
is  simply  a  concrete  stem  wide  enough  to  carry  the  steel. 

Many  theories  have  been  proposed  for  such  beams,  but  the 
latest  and  most  satisfactory  are  those  of  Prof.  Talbot,  in  which 
the  amount  of  steel  is  a  percentage  of  a  beam  having  a  width 
equal  to  the  width  of  the  slab  in  the  T  section,  and  a  depth 


Formulas  for  T  Beams.  31 

found  by  the  usual  methods.  That  is,  the  formulas  already 
given  will  do  for  T  beams  as  well  as  for  ordinary  beams,  but 
in  determining  the  amount  of  steel  it  must  be  a  percentage  of 
such  a  large  area  that  the  writer  has  found  no  resulting  econ- 
omy in  using  such  beams,  especially  when  taken  in  connection 
with  the  objections  mentioned  in  a  later  chapter  concerning 
the  construction  work. 

For  any  reader  who  may  wish  to  investigate  such  beams 
it  may  be  stated  that  the  width  of  the  slab  varies  from  three 
to  five  times  the  thickness  of  the  stem.  Some  men  consider 
the  width  of  the  slab  as  being  the  clear  span,  thus  calling  on 
the  floor  for  compressive  strength  half  way  on  each  side  to 
the  next  support.  T  beams  with  wide  flanges  lack  in  stiffness. 

The  position  of  the  neutral  axis  when  determined  should 
be  such  that  the  thickness  of  the  flange  will  not  be  less  than 
Ys  k,  so  that  the  neutral  axis  may  well  be  in  the  flange  if  de- 
sired. When  the  amount  of  steel  is  determined  it  should  be 
in  as  large  bars  as  possible  in  order  to  have  the  rib  narrow, 
but  the  bond  should  be  carefully  investigated  and  the  steel  have 
enough  peripheral  area  to  furnish  bond.  Web  stresses  also 
are  high  and  should  be  carefully  determined,  and  stirrups  or 
other  web  reinforcement  provided.  Careful  attention  should 
be  paid  that  cross  bearing  steel  is  placed  in  the  slab  across  the 
stem,  in  girders,  or  cross  bearing  beams.  In  the  calculations 
the  rib  is  not  considered  and  its  thickness  depends  upon  the 
size  of  the  steel.  At  its  junction  with  the  floor  slab  a  fillet 
should  be  placed  to  prevent  cracks  because  of  the  sharp  angle. 

Common  values  assigned  to  concrete  and  steel  by  ordinances 
are  as  follows : 

Steel. — Fibre  stress  not  to  exceed  one-third  the  elastic  limit  in 
tension. 

Concrete. — Tension  no  value.  Compression,  500  Ibs.  per  sq.  in. 
for  beams,  350  Ibs.  per  sq.  in.  for  columns. 

Shear. — 50  Ibs.  per  sq.  in.  (as  internal  stress). 

Adhesion  to  steel. — 75  Ibs.  per  sq.  in.  of  surface  of  steel. 

General  rules  for  lengths  of  reinforcing  bars  and  rods  have 
been  given.  The  following  table  gives  the  matter  in  a  little  more 
complete  form.  When  a  certain  fibre  stress  is  assumed  for  the 
steel  and  a  certain  value  given  per  square  inch  for  adhesion,  we 
obtain  the  length  of  steel  necessary  for  bond  by  ascertaining  the 
area  of  the  cross  section  of  the  steel,  multiplying  this  by  the  fibre 


Reinforced  Concrete. 


stress  and  dividing   the  result  by  the   adhesion   per   square   inch, 
multiplied  by  the  circumference  or  perimeter  of  the  rod  or  bar. 

TABLE   V. 

Minimum  lengths  (minimum  clear  span  of  beam)  required  to  secure  rods  and 
bars  against  slipping  under  stated  fibre  stresses  in  the  steel.  Adhesion  75  Ibs. 
per  sq.  inch  of  surface. 


Diameter 
or 

Adhesion  per 
lineal  inch 

10,000 

Yah 
16,000 

ics  of  f  . 
18,000 

20,000 

Bars 

Rods 

Lengths 

M  in. 

75.0 

59.3 

1  ft.    5  in. 

2  ft.    3  in 

2  ft.    7    n. 

2  ft.  10   n. 

%  in. 

112.5 

88.5 

2  ft.    3  in. 

3  ft.    4  in 

3  ft.    9    n. 

4  ft.    2   n. 

y2  in. 

150.0 

117.5 

2  ft.    7  in. 

4  ft.    7  in 

5ft.    2    n. 

5  ft.     8   n. 

*A  in. 

187.5 

147.0 

3  ft.    7  in. 

5  ft.    8  in 

6  ft.    4    n. 

7  ft.     1   n. 

%in. 

225.0 

177.0 

4  ft.    2  in. 

6  ft.    8  in 

7ft.    6    n. 

8  ft.    4   n. 

X  in. 

262.5 

206.0 

4  ft.  11  in. 

7  ft.  10  in 

8  ft.  10  in. 

9  ft.  10  n. 

1  in. 

300.0 

236.0' 

5ft.    7  in. 

8  ft.  11  in 

10  ft.     1  in. 

11  ft.    2   n. 

This  gives  half  the  length  of  the  steel  in  the  beam  (for  there 
are  two,  opposite  and  equal,  pulls)  and  multiplied  by  two  gives 
the  minimum  clear  span  to  be  used  in  connection  with  the  rods 
or  bars.  The  table  shows  this,  and  when  a  beam  has  been  figured, 
the  size  of  the  steel  can  be  taken  readily  from  this  table  in  order 
to  be  safe  as  respects  bond.  One-half  the  lengths  given  in  the 
table  will  be  sufficient  to  run  the  steel  into  walls  or  other  sup- 
ports or  to  lap  pieces  past  each  other.  Of  course,  as  great  a  length 
can  be  used  as  the  designer  wishes,  but  the  lengths  given  are 
minimum.  When  lapping  steel  reinforcement,  the  pieces  should 
not  be  spliced  together  with  wire  so  they  touch  throughout  the 
whole  length,  but  should  preferably  be  so  spliced  that  a  space  be 
left  between  equal  to  their  thickness  or  diameter.  This  is  best 
accomplished  by  bending  each  piece  so  the  pull  will  be  in  a  direct 
line  and  putting  small  spacers  at  intervals  of  a  few  inches.  The 
connection  of  these  lapping  pieces,  however,  should  be  strong 
and  certain  in  order  that  the  concrete  be  not  unduly  stressed  to 
give  the  required  adhesion.  The  spacers  should  be  first-class  metal 
clamps,  similar  to  those  used  for  cables.  The  ideal  lap  is  one 
where  each  end  is  so  bent  that  when  fastened  in  place  the  shape 
will  be  a  loop  similar  to  a  turnbuckle,  with  strong  clamps  at  the 
end  connections  and  several  spacers  across  the  loop.  Another 
good  connection  is  a  screwed  connection.  It  is  really  the  best  if 
properly  made.  It  should  always  be  used  in  columns. 

The  writer  is  a  firm  believer  in  reinforcing  all  beams  on  top 
across  supports.  Unless  means  are  especially  provided  to  localize 
the  stresses,  the  top  of  all  beams  will  exhibit  more  or  less  canti- 


Floor  Slabs.  33 

lever  action,  for  the  connection  causes  it.    In  fact,  it  would  do  no 

harm  to  design  all  beams  in  two  ways:  First,  as  a  plain  beam, 
not  allowing  for  contraflexure ;  second,  as  two  cantilever  beams, 
joined  in  the  middle  of  the  span.  Place  reinforcement  in  the  beam 
accordingly,  turning  it  down  or  up  for  web  reinforcement  when 
it  passes  the  point  where  it  is  required  for  bending  moment  in 
the  top  or  bottom.  Such  a  beam  will  be  safe,  no  matter  how 
loaded,  and  if  a  fire  consumes  the  contents  of  the  room  below  and 
should  happen  to  destroy  the  concrete  protecting  the  under  steel, 
the  steel  in  the  top  of  the  beam  will  carry  the  load.  The  writer 
believes  too  many  chances  have  been  taken  with  reinforced  con- 
crete designing  in  the  past,  and  too  many  chances  are  taken  today. 

Floor  Slabs. 

Owing  to  the  monolithic  character  of  reinforced  concrete 
work  there  is  a  continuous  action  at  supports,  but  it  is  bad  practice 
to  lessen  the  amount  of  bending  moment  developed  at  the  center 
of  beams  or  girders  because  of  it.  Negative  stresses  set  up  at 
supports  is  all  we  can  provide  for  and  this  has  been  touched  upon. 
Therefore,  we  should  take  care  of  the  bending  moment  of  a  simply 

wl2 
supported  beam  at  the  center  by  the  formula,  M  =   —  and  the 

o 

negative  bending  moments  at  the  supports  by  placing  enough  steel 
in  the  top  to  take  care  of  the  bending  moment  as  given  by  the 

wla 
formula,  M  =  TT-. 

With  floor  slabs,  however,  it  is  usual  to  compute  the  bending 

wl8 
moment  by  the  formula,  M  =.  — ,  although  some  designers  use  12 

instead  of  10,  in  which  formula  w  is  the  load  per  square  foot  and  1 
the  span  in  inches,  the  moment,  M,  being  in  inch  pounds.  The  span 
is  always  the  shortest  span  when  the  floor  panel  is  not  square.  If  the 

wla 
panel  is  square  the  formula  is  M  =    —  and  the  reinforcement  runs 

both  ways.  That  is,  when  this  formula  is  used  it  is  figured  that  half 
the  load  goes  to  two  sides  and  the  other  half  to  the  other  two  sides. 
Then  two  layers  of  steel  will  be  used  for  reinforcement,  at  right 
angles  to  each  other.  To  the  thickness  obtained  by  the  formula, 

d==    */ss-  must  be  added  sufficient  concrete  to  protect  the  steel 
V  i^o 

underneath  and  also  the  extra  thickness  caused  by  the  second  layer 
of  steel.  This  additional  concrete  to  allow  for  the  two  layers  of 


34 


Reinforced  Concrete. 


steel   is   often  overlooked  by  designers,   with   the   result   that   the 
moment  arm  is  shortened  and  the  slab  deflects  unduly. 

Mr.  Robert  B.  Hansell,  C.  E.,  Baltimore,  Md.,  has  asked  the 
writer  to  insert  the  following  table  in  order  to  make  it  clear  that 
in  the  case  of  a  uniformly  loaded  beam  supported  at  several  equi- 
distant points  the  portion  of  the  load  bearing  on  each  support  is  as 
follows : 

TABLE  VI. 


Number 
of 
supports. 

1st. 

Num 
2d. 

Der  of  each 
3d. 

support. 
4th. 

5th. 

6th. 

2 
3 
4 
5 
6 

'/a 

X 

4/10 
11/28 
15/38 

H. 

10/8 
11/10 
32/28 
43/38 

H 

11/10 
26/28 
37/38 

4/10 
32/28 
37/38 

11/28 
43/38 

15/38 

It  is  seldom  that  more  than  three  supports  will  occur  in  prac- 
tice, but  the  above  table  will  be  useful  in  helping  distribute  the  load 
to  all  the  beams  under  floor  and  roof  slabs.  The  load  per  square 
foot  on  the  slab  will  be  the  assumed  floor  loading,  and  the  load  per 
lineal  foot  on  the  beams  and  girders  under  the  slab  will  be  deter- 
mined by  the  reactions  shown  in  the  above  table. 

To  space  the  rods  equally  both  ways  in  a  square  slab  is  not 
correct,  for  if  we  consider  a  12"  strip  as  the  unit  and  the  floor 
consists  of  a  number  of  12"  strips  side  by  side  we  know  that  the 
diagram  for  bending  moment  will  be  a  parabola.  The  steel  should 
therefore  be  closer  together  in  the  middle  running  both  ways.  To 
determine  this  draw  the  beam  and  the  parabola  with  the  vertex  as 
M.  Then  dividing  the  beam  into  a  number  of  12"  sections  determine 
the  bending  moment  on  each.  Reinforce  each  for  its  bending 
moment.  While  thjs  is  a  little  labor  and  there  may  be  some  diffi- 
culty in  securing  the  right  spacing  of  the  steel  it  is  more  correct 
than  the  usual  method.  When  a  floor  slab  freely  supported  at  all 

wla 
four   sides,    designed    for   a   bending   moment    expressed    by     — 

O 

develops  so  much  strength  that  the  use  of  10  as  a  divisor  seems  to 
fit  better  than  8,  part  of  the  reason  is  in  the  excess  of  steel  in  the 
outer  edges  of  the  slab. 

In  this  connection  see  end  of  Chapter  II. 


Reinforced    Concrete. 


34a 


CHAPTER  I.— (Continued.) 
PARABOLIC  THEORY  OF  STRESS. 

It  has  been  mentioned  in  the  preceding  pages  that  for  economy 
in  design  the  formulas  there  given  do  not  give  the  best  results.  In 
fact  for  the  ideal  beam  the  cost  of  the  steel  should  exactly  balance 
the  cost  of  the  concrete  above  the  center  of  the  steel.  Certain  obvi- 
ous considerations  prevent  the  attainment  of  this  ideal  but  by  using 
what  is  known  as  the  Parabolic  Theory  of  Stress,  it  can  be  more 
closely  approximated  than  by  the  straight  line  theory  given  under 
Fig.  2  on  page  12. 

When  we  study  the  stress  strain  curve  of  a  reinforced  con- 
crete beam  it  is  easily  seen  that  the  material  does  not  act  so  that 
the  unit  deformation  in  any  horizontal  fiber  varies  directly  as  its 
distance  from  the  neutral  axis.  In  fact  the  tensile  strength  of  the 
concrete  is  gone  by  the  time  the  steel  is  stressed  up  to  about  one- 
fourth  the  usual  working  stress,  and  this  is  shown  by  innumerable 
small  cracks  in  the  bottom  under  the  steel.  By  the  time  the  steel  is 
stressed  to  the  elastic  limit  it  is  believed  the  cracks  extend,  almost, 
if  not  quite,  to  the  neutral  axis. 

Neglecting  therefore  the  tensile  strength  of  the  concrete  and 
concentrating  the  entire  tensile  stress  in  the  line  of  steel  near  the 
bottom  the  straight  line  theory  for  the  steel  is  correct,  so  that  no 
matter  what  formula  may  be  used  to  determine  the  resisting  moment 
as  determined  by  the  concrete,  the  resisting  moment  as  determined 
by  the  steel  is  always 

M  =  f  p  d'b  d'=f  A  d'd 

which  is  the  formula  given  on  page  22,  which  unfortunately  contains 
a  typographical  error. 

By  testing  reinforced  concrete  beams  to  destruction  and  plot- 


FIG. 


ting  the  results  we  obtain  a  stress  strain  curve  for  the  concrete  in 
compression  closely  approximating  a  parabola.     The  agreement  ti 


S4b  Parabolic   Theory  of  Stress. 

so  remarkable  that  the  parabola  has  been  chosen  as  representing 
more  nearly  the  actual  stress  strain  curve  than  the  triangle.  This 
is  shown  in  Fig.  3A. 

To  illustrate  the  difference  this  makes,  the  following  formulas 
are  used  to  give  the  exact  stresses  in  the  beam. 

The  average  abscissa  of  a  triangle  equals  one-half  the  greatest 
but  the  average  abscissa  of  a  parabola  equals  two-thirds  the  great- 
est so  that  the  equation  on  page  12  becomes,  for  the  parabolic  for- 
mula 

fp=  2/3  ck 

The  formula  for  determining  the  position  of  the  neutral  axis 
in  the  straight  line  formula  is  given  on  page  13,  and  this  becomes, 
for  the  parabolic  formula, 


k  =»  V3pn  +  (fpn)8  —  f  pn 

In  a  triangle  the  center  of  gravity  is  one-third  the  height  from 
the  base,  which  gives  k/3,  as  shown  on  page  13.    In  a  parabola,  how 
ever,  the  distance  is  3/8,  so  that,  for  the  parabolic  formula, 
d'  =  l--3/8  k 

It  is   easy  to   remember   the   parabolic    formulas    for   ultimate 
loads  by  simply  substituting  3/8k  for  l/3k  and  by  substituting  2/3 
for  1/2  when  dealing  with  the  stresses  in  concrete.    The  moment  of 
resistance  for  the  beam  as  determined  by  the  concrete  is 
M  =  2/3kd'dbd8 

Another  very  important  difference  must  be  pointed  out.  The 
material  deficient  in  area  determines  the  strength  of  the  beam.  If 
the  steel  is  deficient  in  area  the  parabolic  formulas  for  ultimate 
loads  cannot  be  used  for  they  are  based  upon  the  possibility  of  uti- 
lizing the  full  strength  of  the  concrete.  It  is  only  when  the  steel 
"balances"  the  concrete  that  the  resisting  moment  for  the  steel  gives 
the  exact  resisting  moment  for  the  beam.  With  parabolic  formulas 
we  should  not  use  less  than  one  per  cent  of  steel  and  some  beam? 
require  nearly  two  per  cent.  With  straight  line  formulas  we  can 
use  as  small  a  per  cent  of  steel  as  desired.  This  statement,  of 
course,  must  be  modified  by  thel character  of  concrete  used,  for  a 
very  small  per  cent  of  steel  will  develop  the  full  strength  of  some 
concretes. 

Using  straight  line  formulas  we  secure  rigidity  and  a  certain 
excess  of  concrete.  The  advantage  is  that  when  a  beam  is  under- 
reinforced  (has  too  small  an  area  of  steel  to  balance  the  concrete) 
it  gives  warning  long  before  it  breaks.  A  "balanced"  beam  goes  sud- 
denly. This  partly  accounts  for  the  general  use  of  straight  line 
formulas  in  building  laws.  Another  reason  they  are  greatly  used  i* 


Reinforced   Concrete.  34c 

that  the  formulas  in  general  use  up  to  within  a  year  or  two  were 
empirical  and  in  this  form,  so  that  the  majority  of  designers  used 
rhem.  Another  reason  is  that  until  within  the  same  time  few  engi- 
neers or  architects  could  procure  simply  written  books  on  rein- 
forced concrete  design.  The  greater  part  of  the  information  was 
given  free  by  companies  selling  steel.  To  prevent  the  charge  of 
trying  to  sell  too  much  steel  they  all  used  straight  line  formulas 
and  advocated  small  percentages  of  reinforcement.  Now,  however, 
that  it  is  generally  known  "the  more  steel  the  less  concrete"  and 
that  the  concrete  costs  about  three  times  as  much  as  the  steel  in  a 
beam,  the  steel  companies  are  generally  using  parabolic  formulas. 

With  straight  line  formulas  we  are  limited  to  the  use  of  work- 
ing stresses  in  both  steel  and  concrete  with  vague  ideas  as  to  the 
actual  factor  of  safety.  With  parabolic  formulas  the  beam  is  sup- 
posed to  contain  enough  steel  to  develop  the  full  strength  of  the 
concrete  by  the  time  the  steel  stress  equals  the  elastic  limit. 

The  straight  line  theory  is  therefore  known  as  the  Fiber  Stress 
Method  and  the  parabolic  theory  is  known  as  the  Factor  of  Safety 
Method.  As  we  have  here  two  materials  differing  in  many  re- 
spects, joined  together  in  a  structure  the  factor  of  safety  method 
seems  most  logical  to  use  for  economic  design.  Therefore,  instead 
of  designing  to  obtain  a  resisting  moment  equal  to  the  bending  mo 
ment,  with  safe  fiber  stresses  in  the  two  materials,  the  bending  mo- 
ment produced  by  the  load  should  be  multiplied  by  the  desired  fac- 
tor of  safety  to  get  the  ultimate  bending  moment.  Then  instead  of 
a  safe  fiber  stress  in  the  concrete  the  actual  or  assumed,  ultimate 
strength  is  used.  Instead  of  a  safe  fiber  stress  in  the  steel  the 
elastic  limit  is  vised.  The  resisting  moment  obtained  is  equal  to 
the  ultimate  bending  moment. 

To  secure  the  maximum  economy  in  design  when  a  test  load  is 
prescribed  some  ambitious  designers  assume  a  load  equal  to  the  test 
load  plus  the  estimated  dead  load  of  the  beam  or  slab.  To  obtain 
the  resisting  moment  they  assume  a  strength  for  the  concrete  of 
about  two-thirds  the  actual  or  assumed  strength.  For  the  steel  they 
assume  a  stress  about  five  per  cent  less  than  the  elastic  limit.  This 
insures  the  beam  against  failure  under  the  test  load.  It  would 
hardly  do  to  require  the  test  load  to  stress  the  concrete  to  the  ulti- 
mate and  the  steel  to  the  elastic  limit  or  beyond,  yet  it  is  too  often 
done  in  competitive  designing. 

Straight  line  formulas  give  a  certain  stress  in  the  concrete  un- 
der load.  The  stress  is  actually  about  fifteen  per  cent  less  when  we 
calculate  it  by  parabolic  formulas.  Thus  there  is  really  a  larger 
factor  of  safety  under  working  loads  than  is  apparent. 


34d 


Parabolic    Theory  of  Stress. 


A  table  like  Table  I  can  be  calculated  for  parabolic  formulas  by 
using  the  formula  for  k  already  given ;  that  is, 

k  —  V3pn  +  (fpn)2  —  |  pn 

To  calculate  a  table  like  Table  II  to  ascertain  the  value  of  "k'' 
in  connection  with  unit  stresses,  use  the  formula 

k  =  ^_f 
ks=  2c 

in  which 

k  =  depth  to  neutral  axis ; 

f  =  elastic  limit  of  steel; 

c  =  ultimate  strength  of  concrete; 

p  =  ratio  of  steel  to  concrete. 

A  table  of  moment  factors  "K,"  like  Table  III  can  be  calculated 
by  the  formula 

K  =  2/3cd'k 

which  is  similar  to  the  formula  given  on  page   16,  using  2/3  in- 
stead of  1/2. 

Analysis  of  Beams  and  Slabs. 

When  a  beam  or  slab  shows  signs  of  failure  and  it  is  possible 
to  ascertain  the  area  of  the  reinforcement,  parabolic  formulas  are 
used  to  analyse  the  failure  if  the  steel  is  shown  to  be  in  excess  of 
or  balances  the  concrete.  If  the  steel  is  confessedly  inadequate  then 
use  straight  line  formulas.  We  do  not  care  about  the  actual  stress 
in  the  material  in  excess. 

Instead  of  straight  line  formulas,  however,  the  flexure  formu- 
las of  Professor  Talbot  may  be  used.  They  are  parabolic  also  and 
we  can  use  them  practically  as  straight  line  formulas  but  instead  of 
taking  a  definite  fiber  stress,  a  fraction  "q"  is  used. 


FIG.  3B. 
In  Fig.  3B  the  diagram  on  the  left  shows  c'  which  is  the  ulti- 


Reinforced    Concrete. 


34e 


mate  strength  of  the  concrete  in  compression  and  "c"  the  strength 
the  concrete  reaches  at  the  time  the  strength  of  the  steel  (the  elastic 
limit)  is  reached.  Instead  of  assuming  the  strength  of  the  steel  at 
the  elastic  limit  any  assumed  strength  can  be  given  to  it,  thus  ap- 
proximating the  safe  fiber  stress  if  desired.  The  diagram  on  the 
right  is  the  deformation  diagram  in  which  "e'"  is  the  total  defor- 
mation in  the  concrete  at  the  time  of  failure,  and  "e"  the  deforma- 
tion reached  when  the  steel  has  reached  the  strength  assumed.  At 
the  bottom  of  the  diagram  "f"  is  the  steel  stress  and  "fe"  the  defor- 
mation in  the  steel.  The  fraction  "q"  stands  for  ~^r.  For  example, 
when  "q"  =  l/4:  the  concrete  is  strained  to  one- fourth  its  limit  of 
compression,  etc. 


1 


0       . 

. 

i    . 

3     .' 

1-     . 

'f      . 

&   . 

ft     .« 

. 

0 

B 

x 

^ 

/ 

/o.r 

x 

x 

/ 

'•H 

x 

x 

/ 

X 

X 

/ 

A 

133 

/ 

X 

X 

$ 

/ 

x 

x 

^ 

2a- 

/ 

^ 

X 

1 

2.8 

A 

^ 

? 

5.5 

5- 

A" 

x 

o 

5/A 

•ess 

"» 

/Af 

1C 
/> 

w 

^7 

FI 

2C 

G. 

00 

3C 

Fig.  3C  is  a  diagram  taken  from  the  bulletins  from  the  Illinois 
Experiment  Station  containing  the  reports  of  tests  made  under  the 
direction  of  Professor  Talbot,  with  some  additional  notes. 

These  flexure  formulas  are  rather  unwieldly  and  are  therefore 
a  method  of  analysis  rather  than  for  designing.  By  using  them  to 
construct  diagrams  they  can  be  of  great  service  but  for  every  day 
work  the  straight  line  formulas  are  all  right  for  partial  loads,  below 
the  ultimate. 


84f  Parabolic   Theory  of  Stress. 

The  idea  in  view  in  developing  these  flexure  formulas  for  loads 
below  the  ultimate  is  to  keep  the  stress  in  the  steel  below  the  yield 
point  (elastic  limit)  and  yet  ascertain  the  real  stress  in  the  concrete. 
By  assuming  different  values  for  "q"  the  actual  stress  in  the  con- 
crete for  any  assumed  stress  in  the  steel  can  be  found,  irrespective 
of  the  percentage,  or  area,  of  reinforcement.  Thus  it  may  be  seen 
that  the  factor  of  safety  method  and  the  fiber  stress  method  are 
practically  combined. 

To  show  how  the  foregoing  simple  formulas  are  complicated 
by  the  introduction  into  them  of  "q"  the  expression  on  page  12,  be- 
comes 

kc  (3  -  q) 

fp"Tc2^ir 

and  that  at  the  bottom  of  page  13  becomes 


i  I  2  —      " 

*\  3-q  "    V3-q/          3-q 

Stress  Strain   (Stress  Deformation)  Curve. 

In  analytical  mathematical  work  every  line  described  by  its 
relation  to  an  origin,  that  is  by  ordinates  and  abscissas,  is  termed  a 
curve,  even  when  it  is  a  straight  line. 

Stress  is  a  force  applied.  Strain  is  a  deformation  resulting 
from  that  stress.  Deformation  is  amount  of  change  of  form  or 
shape. 

On  a  sheet  of  squared  paper  let  the  vertical  graduations  upward 
from  zero,  represent  the  deformation  and  the  horizontal  gradua 
tions  from  left  to  right,  represent  the  stress.  When  points  are 
plotted  showing  the  deformation  for  any  stress  and  all  the  points 
are  joined  we  have  a  stress  strain  curve.  As  already  mentioned  the 
stress  strain  curve  for  the  concrete  in  compression  in  a  reinforced 
concrete  beam  approximates  a  parabola  in  form. 


FIG.  3D. 
Fig.  3D  shows  a  parabola,  which  is  a  curve  such  that  any  point 


Reinforced   Concrete.  34g 

on  the  curve  is  equi-distant  from  a  given  point  and  a  given  straight 
line.  The  given  point,  S,  is  called  the  focus  and  the  given  straight 
line,  A — B,  the  directrix. 

CD  =  DS;MP  =  PS;EF  =  FS. 

The  point  O  is  called  the  vertex  and  when  the  directrix  touches 
fhe  vertex,  O,  the  equation  for  the  parabola  is 
y2  =  4x 
y  =±2yT 

The  general  equation  for  the  parabola  with  any  other  position 
of  the  directrix,  is 

ya  =  4  ax 
y  =  ±  2  Vax 

In  Fig.  3C.  the  position  in  which  the  parabola  is  drawn  is  that 
in  which  it  is  generally  drawn  when  plotted  as  a  stress  strain  curve 
of  the  concrete  in  compression.  The  stress  is  represented  by  "x" 
and  the  deformation  by  "y".  In  this  diagram  for  convenience  the 
ultimate  strength  of  the  concrete  is  assumed  at  2000  Ibs.  per  sq.  in. 
and  the  deformation  per  unit  —  0.002  =  e. 

Ratio  of  Deformation. 

Over  the  modulus  of  elasticity  much  discussion  has  been  waged 
and  as  concrete  has  no  true  modulus  of  elasticity  the  ratio  known  as 
"the  ratio  between  the  moduli  of  elasticity  of  the  concrete  and  steel" 
should  really  be  termed  "the  ratio  of  deformation."  No  one  objects 
to  the  statement  that  some  ratio  of  deformation  exists  but  decided 
objection  is  made  to  that  ratio  being  termed  the  ratio  between 
moduli  of  elasticity  when  one  of  the  materials  has  no  such  modulus. 

This  ratio  of  deformation  is  expressed  in  terms  of  a  tangent  to 
the  parabola  representing  the  stress  strain  curve  of  the  concrete  in 
compression.  The  stress  is  the  tangent  of  an  angle  between  the 
deformation  and  the  tangent  to  the  parabola:  essentially  the  co- 
tangent. 

When  the  concrete  commences  to  deform  the  stress  strain  curve 
is  almost  straight  but  gradually  changes  in  shape,  becoming  more 
nearly  vertical  until  when  the  limit  of  deformation  is  reached  it 
has  assumed  a  parabolic  form  as  shown  in  Fig.  3C. 

The  line  representing  the  initial  modulus  of  elasticity  is  repre- 
sented by  the  line  A — C  and  is  tangent  to  the  parabola  at  its 
origin.  This  origin  is  not  that  usually  assumed  as  the  origin  of  the 
parabola  but  is  the  origin  of  the  stress  strain  curve  of  compression 
in  the  concrete. 

In  Fig.  3E  let  x  and  y  represent  respectively  the  abscissa  and 


34h 


Parabolic    Theory  of  Stress. 


ordinate  of  the  parabola.  PT  represents  the  tangent  at  the  point 
where  intersected  by  y,  and  a  is  the  angle  of  the  tangent,  dx  is  an  in- 
finitesimal increment  of  x  and  dy  is  an  infinitesimal  increment  of  y. 


M 


N 

FIG.  3E. 

Plotting  them  as  shown  we  obtain  the  triangle  P,  Q,  R  in  which 
to  find  the  angle  P  =  da.  Then  dy/dx  gives  the  tangent  of  the 
angle  P. 

Conceive  the  quantities  dx  and  dy  as  being  so  small  that  the 
line  P  Q  extended  to  T,  will  assume  the  position  P  T,  swinging  as 
indicated  by  the  arrows. 

y 

At  this  poinl      ~p=    which   represents  the  slope   of  the  curve. 

being  coincident  with  dy/dx,  which  represents  the  slope  of  the  line, 
gives  the  following  equation  for  the  tangent  of  the  parabola 

Tan  a  =  y/2x 

The  angle  b  is  one  used  to  express  the  value  of  EC.  In  Fig.  3D 
it  is  marked  A  and  the  angle  for  which  we  have  just  found  the 
equation  for  the  tangent,  is  marked  C. 

Tan  b  =  EC 
2c 

y  =  e  c  =  £  Ece 

When  different  values  of  n  are  used  they  of  course  represent 
the  EC  obtained  from  different  points  of  tangency  but  instead  of  the 
line  being  tangent  to  the  parabola  at  the  point  fixed  by  the  selected 
concrete  fiber  stress,  it  is  parallel  to  said  tangent  and  starts  from 
the  point  of  origin  of  the  stress  strain  curve. 

As  a  matter  of  fact  the  line  forming  the  side  of  an  angle,  the 
tangent  of  which  represents  the  modulus  of  elasticity  of  the  con- 
crete cannot  be  tangent  to  the  parabola  at  a  point  where  the  con- 
crete stress  =  0.  It  must  be  a  tangent  at  some  definite  value  of  the 
stress  in  the  concrete. 


2  x 

Let  —  =  Tan  b 


CHAPTER  II. 

LOADS  ON  BEAMS. 

This  chapter  is  intended  as  a  review  for  the  reader  and  an  aid 
for  quick  reference  when  some  useful  and  necessary  formula  is  for- 
gotten. 

A  moment  is  the  product  of  a  force  multiplied  by  the  distance 
at  which  it  acts.  For  example,  a  load  suspended  from  the  extreme 
end  of  a  cantilever  beam  causes  it  to  bend  more  than  if  placed  near 
the  fast  end.  That  is,  the  bending  moments  vary  with  the  distance 
from  the  load  to  the  support.  The  bending  moment  is  opposed  by 
a  resisting  moment  in  the.  beam. 

When  the  resisting  moment  is  less  than  the  maximum  bending 
moment  the  beam  fails.  When  one  is  equal  to  the  other  the  beam 
has  no  factor  of  safety.  The  factor  of  safety  is  represented  by  the 

Rm 
fraction  ~^f",  where 

M  =  maximum  bending  moment. 

Rm  =  resisting  moment  of  beam. 

When  a  beam  is  designed  to  carry  a  load  four  things  are  to  be 
considered : 

1st.  Reactions.  This  is  the  name  given  to  the  proportion  of 
the  load  carried  by  each  support.  The  name  is  given  because  action 
causes  reaction  and  it  is  convenient  to  assume  that  there  is  an  up- 
ward push  at  the  supports  to  balance  the  downward  push  of  the 
beam  with  its  load. 

2d.     Bending  moment. 

3d.  Deflection.  While  a  beam  may  be  strong  enough  to  carry 
a  certain  load  it  may  deflect,  or  bend,  enough  to  crack  plastering. 
Consequently  there  are  cases  where  deflection  is  of  more  importance 
than  absolute  strength.  Formulas  for  deflection  will  not  be  here 
considered  in  connection  with  reinforced  concrete  beams.  If  the 
design  calls  for  a  stress  in  the  concrete  not  exceeding  600  Ibs.  per 
sq.  in.  and  not  exceeding  16,000  Ibs.  per  sq.  in.  in  the  steel  the  de- 
flection will  not  exceed  1/360  of  the  distance  between  supports. 
This  is  a  limit  beyond  which  it  is  hardly  wise  to  go  if  the  under  side 
of  the  beam  is  to  be  plastered. 

35 


36  Reinforced  Concrete. 

4th.  Shear.  This  is  a  term  applied  to  the  action  tending  to 
cut  the  beam  vertically  and  is  caused  by  the  downward  push  of 

the  load  resisted  by  the  upward  push  of  the  supports.  1-2-4  concrete 
can  safely  stand  300  Ibs.  per  sq.  in.  of  such  action. 

What  is  termed  shear  in  a  beam  of  reinforced  concrete  is 
really  diagonal  tension.  When  a  beam  bends  the  bottom  fibres 
stretch  and  the  upper  fibres  are  compressed.  At  the  neutral  axis 
there  is  a  tendency  to  shear,  and  this  grows  less  toward  the  top 
and  bottom  of  the  beam,  where  one  set  of  stresses,  of  course,  over- 
comes the  effect  of  the  other  set.  Shear  in  this  case  should  not 
exceed  60  Ibs.  per  sq.  in. 

Having,  then,  two  sets  of  forces  acting  at  continually  chang- 
ing angles  with  each  other,  we  have  resultants  to  these  forces  act- 
ing at  right  angle  to  the  tangent  of  the  curve  formed.  The  re- 
sultant acts  as  a  tensile  stress  in  the  concrete  and  stirrups  are 
placed  at  right  angles  to  it. 

This  explains  why  stirrups  should  be  fastened  in  some  way  to 
the  bottom  rods,  or  hooked  under  them,  and  why  they  should  go 
farther  than  the  top  of  the  beam;  for  as  put  in  many  beams,  the 
stirrups  are  too  short  for  bond.  See  Chap.  I. 

Let  W  =  total  load  in  pounds,  uniformly  distributed,  including  the 

weight  of  the  beam  =  wl  -f-  w'l. 
w  =  load  per  lineal  foot  on  beam. 
w'=  weight  per  lineal  foot  of  beam. 
P  =  concentrated  load  on  beam. 
B  ==  total  weight  of  beam  =  w'l. 
1  =  length  in   inches  of  beam.     This  is   usually  assumed  as 

equal  to  the  clear  width  between  supports  plus  a  bearing  at 

each  end,  as  it  gives  a  better  margin  of  safety  than  when 

the  clear  span  alone  is  used. 
M  =  maximum  bending  moment  in  inch  pounds. 

Case  A.  Beam  supported  at  both  ends  (freely  resting  on  sup- 
ports) and  loaded  uniformly. 

Wl 
M=  ~g",  at  middle  of  beam. 

W 

Maximum  shear  at  points  of  support  =  ~2~. 

When  the  shear  acts  upward  on  the  left  side  of  a  section,  or 
downward  on  the  right  side,  it  is  termed  positive.  The  reverse  case 
gives  negative  shear.  As  all  beams  are  subjected  to  positive  and 
negative  shear  there  is  a  point  where  the  sign  changes,  and  this  is 
where  the  maximum  bending  moment  occurs. 


Loads  on  "Beams. 


L  on  DING  s . 


OOODOOOOOQQO. 


clnnnnononnhJ 


T| 

^^^^ 

Q 

ft 

_TTT  .~r-  .  T-T-   •*-   ~cJ      j 

f] 

Load  M~^ 

7                                          5 

-*-* 

^**  " 

<?  /- 

of  leam,same  as  Cffse  H. 


D. 


FIG,  4 — BEAM  I/DADINQS. 


38  Reinforced  Concrete. 

On  the  left  half,  the  shear  is  positive  and  on  the  right  half  nega- 
time,  and  0  at  middle  of  beam. 

W 

Reaction  at  each  support  =  -g". 

Case  B.  Beam  supported  at  both  ends  with  load  concentrated 
at  the  middle. 

PI  Bl 

M  =   -£-    +    -g~,    at  middle  of  beam. 

P  +  B 
Max.   shear  at  points  of  support  =  — ^ —  and  at  middle  of 

beam  =  0. 

T>     I     T> 

In  this  case   (B)   the  shear  at  all  points  on  the  beam  =      "jT 

P  +  B 
Reaction  at  each  supports  — ^ — . 

Case  C.     Cantilever  beam  uniformly  loaded. 

Wl 
M  =  -g"  at  point  of  support. 

Maximum  shear  at  point  of  support  ==W. 
Reaction  at  point  of  support  =  W. 

Case  D.     Cantilever  beam  with  load  concentrated  at  any  point. 
In  this  case  1  =  distance  from  point  of  support  to  a  vertical 
line  through  center  of  gravity  of  load. 

Bl 
M  =  PI  +  -g-  at  point  of  support. 

Max.  shear  at  point  of  support  =  P  -f  B. 

Reaction  at  point  of  support  =  P  -f-  B. 

Case  E.  Beam  supported  at  both  ends  with  load  concentrated 
at  any  point. 

Call  distance  from  left  support  to  load,  a,  and  from  right  sup- 
port to  load,  b.  ' 

a(2Pb  +  Bl-Ba) 
M  =  —         — gj —          — ,  under  load. 

Pb         B 

Max.  shear  at  support  a  =  ~j~  +  "2". 

P  a 

«  «        u  K        t  |        D 

12- 

Reaction  at  each  support  equal  to  shear. 

At  this  point  the  general  rules  for  shear  and  reactions  may  be 
introduced. 

The  weight  of  the  beam  being  a  distributed  load,  one-half  goes 
to  each  support  in  addition  to  the  proportionate  part  of  the  loads 


Loads  on  Beams. 


39 


on  the  beam.  In  shear  one-half  is  plus  (the  left)  and  one-half  is 
minus  (the  right). 

Rule  for  reactions  for  combinations  of  loads.— Multiply  each 
load  by  its  distance  from  one  support.  Add  the  products  and  di- 
vide the  sum  by  the  span.  This  gives  the  reaction  on  the  opposite 
support.  The  other  reaction  is  obtained  by  subtracting  the  reaction 
thus  found  from  the  sum  of  the  weights  of  the  loads.  The  sum  of 
the  reactions  is  always  equal  to  the  sum  of  the  loads. 

Rule  for  shear  for  combination  of  loads. — The  maximum  shear 
will  equal  the  greater  reaction.  The  shear  under  each  load  is  found 
by  setting  down  either  reaction  with  its  plus  or  minus  sign  and 
adding,  algebraically,  to  it  successively  the  weights  of  the  loads, 
commencing  with  the  one  nearest  the  reaction  chosen. 

Case  F.  Beam  supported  at  both  ends  with  two  loads  equally 
distant  from  the  ends. 

Call  the  distance  from  each  end,  a. 

Bl 

M  =  Pa  -f-  ~g-   at  middle  of  beam. 

2P  +  B 
Max.  shear  at  points  of  support  = „ . 

B 

Reaction  at  each  support  =  P  +  ~2~» 

Case  G.  Beam  supported  at  both  ends  with  several  concen- 
trated loads. 


FIG.  5— CASE  G. 

The  most  simple  method  for  this  case  is  to  make  a  scale  draw- 
ing, showing  by  a  single  horizontal  line  the  length  of  the  beam. 
Calculate  each  M  as  shown  for  case  E.  Draw  vertical  lines  down- 
ward under  each  load,  the  lengths  of  the  lines  under  each  load  rep- 
resenting the  bending  moment  caused  by  the  load  at  that  point. 
Connect  the  lower  ends  of  these  lines  to  the  ends  of  the  beam.  This 


40  Reinforced  Concrete. 

gives  a  number  of  triangles  equal  to  the  number  of  loads,  and  each 
vertical  line  will  be  divided  into  the  same  number  of  sections. 

Add  the  lengths  of  these  sections  together  to  obtain  the  bend- 
ing moment  at  each  point.  In  other  words,  the  total  bending  mo- 
ment at  any  point  produced  by  the  weights  of  all  the  loads  is  equal 
to  the  sum  of  the  moments  at  that  point  produced  by  each  of  the 
weights  separately. 

Under  each  load  extend  the  vertical  line  until  it  is  equal  in 
length  to  the  bending  moment  at  that  point  caused  by  all  the  loads. 
Connect  the  ends  of  these  lines  and  the  ends  of  the  beam.  Above 

T51 

the  beam  draw  a  parabola  with  an  extreme  height  =~g~.  The  posi- 
tion and  amount  of  the  maximum  bending  moment  will  be  found 
by  scaling  the  longest  possible  vertical  line  intercepted  by  the  para- 
bola above  and  the  irregular  figure  below  the  beam. 

Case  H.    Beam  fixed  at  both  ends  and  loaded  uniformly. 

A  beam  supported  at  the  ends  bends  downward  when  loaded 
and  is  concave  on  top.  When  fixed  at  the  ends  it  is  convex  on  top 
at  each  end  and  concave  in  the  middle.  When  uniformly  loaded  the 
points  of  contraflexure  are  0.2113  the  length  from  each  support. 

**      Wl 

M  =  -|2~  at  points  of  support. 

Wl 
M=-g4-  at  middle  of  beam. 

W 
Max.  shear  =  -g-  at  points  of  support. 

Case  I.  Beam  fixed  at  both  ends  with  concentrated  load  in 
middle. 

Points  of  contraflexure=0.25  the  length  from  each  support 

PI        Bl 
M=-g--f-j7j-  at  points  of  support. 

PI        Bl 
M  =~g~  -f-  ~2f  at  middle  of  beam. 

•p    l      T> 

Max.  shear  = — <•> — at  points  of  support 

Parallel  Forces  on  Simple  Beams. 

All  the  forces  acting  on  a  beam  may  be  determined  graphi- 
cally and  thus  the  foregoing  formulas  proven.  Combinations 
can  be  worked  out  without  the  labor  of  going  through  the  cal- 
culations and  the  work  will  prove  itself. 

Let  A  B  represent  a  beam  resting  on  supports  as  shown 


Loads  on  Beams. 


41 


by  the  arrows  pointing  upward  at  C  and  D,  these  arrows  rep- 
resenting the  reactions.  At  the  left  the  line  A'  B'  is  the  sum 
of  all  the  weights  drawn  to  some  scale,  each  weight  being  rep- 
resented by  the  amount  between  the  figures,  e.  g.,  from  A'  to  1 
is  force  1;  from  1  to  2  is  force  2,  etc.  The  line  T  O  is  per- 
pendicular to  the  line  A'  B'  and  is  of  any  length,  generally 
taken  at  some  even  number  of  hundreds  or  thousands  of  pounds, 
depending  upon  the  scale  to  which  A'  B'  is  drawn.  From  O 
draw  lines  to  1,  2,  3,  etc.,  and  to  the  ends.  With  triangles  or 
parallel  ruler  transfer  these  lines  to  form  the  polygon  a,  1,  2, 
3,  4,  b,  under  the  beam.  Connect  the  points  a  and  b  and  trans- 
fer the  line  so  it  will  be  represented  in  direction  by  the  line  O  S. 


FIG.  6 — PARALLEL  FORCES  ON  BEAM. 

Then  the  reaction  under  A  is  shown  by  C  =  A'  S,  and  the 
reaction  under  B  is  shown  by  D,  =  B'  S,  to  scale. 

_The  bending  moment  at  any  point  is  equal  to  the  length 

of  OT  multiplied  by  the  ordinate  of  the  polygon  at  that  point. 
For  example,  the  bending  moment  at  2  is  equal  to  OT  multi- 
plied by  f2.  If  our  scale  is  in  hundreds  of  pounds  and  the 


~Tr»'"ri  ^^?>*5:>>x^ 

(OF  THE     *^\ 
-'NIVERSiTY  1 


OF 


42  Reinforced  Concrete. 

length  OT  is  equal  to  one  unit  of  the  scale,  then  the  ordinate 
is  equal  to  the  bending  moment. 

Shear  is  obtained  by  the  third  diagram  with  the  shaded 
rectangles.  The  construction  of  this  figure  needs  little  explana- 
tion. Simply  produce  the  horizontal  and  vertical  lines  as 
shown  and  hatch  the  rectangles  thus  formed.  The  shear  at 
any  point  on  the  beam  is  equal  to  the  length  of  the  longest 
vertical  line  at  that  point.  The  diagram  shows  that  the  point 
of  maximum  bending  point  is  the  point  where  the  shear  equates 
to  zero. 

To  consider  the  weight  of  the  beam,  which  is  uniformly 
distributed,  it  will  be  well  to  make  a  separate  diagram  and  after- 
ward take  the  sums  of  the  moments,  shears  and  reactions, 
caused  by  this  distributed  load  and  the  concentrated  loads 
shown  by  the  arrows.  This  is  shown  in  other  figures. 

In  calculating  a  beam,  the  load  per  lineal  foot  is  used  as  ex- 
plained in  the  formulas.  In  calculating  a  floor  slab,  consider  it  as 
a  number  of  beams  12  inches  wide  lying  side  by  side.  It  is  thus 
necessary  to  figure  only  one  12-inch  beam  in  order  to  ascertain 
thickness  of  slab  and  amount  of  steel.  Retaining  walls  may  be 
calculated  as  a  series  of  horizontal  beams,  one  on  top  of  another, 
or  as  a  series  of  vertical  beams  standing  edge  to  edge  on  end.  To 
secure  proper  intervals  in  slabs,  it  is  customary  to  have  reinforce- 
ment at  right  angle  to  the  principal  reinforcement,  to  which  the 
latter  will  be  connected  by  wiring  at  intersections.  This  crossing 
steel  is  generally  assumed  as  being  equal  to  one-third  of  1  per 
cent  of  the  area  and  spaced  accordingly.  Where  the  extremes 
of  temperature  are  not  great,  even  less  than  this  amount  may  be 
used.  Bars  of  the  same  size  are  used,  which  would  mean  that 
when  the  reinforcement  in  the  line  of  the  beam  is  1  per  cent,  the 
bars  are  spaced  six  inches  apart;  then  the  crossing  bars  will  be 
18  inches  apart.  Nothing  is  settled  about  this  point  yet,  and 
two  considerations  enter  into  the  question.  One  is  temperature 
and  the  necessity  for  some  provision  to  avoid  temperature  cracks. 
The  other  is  shear  in  the  concrete  between  adjacent  beams  of 
which  the  floor  is  assumed  to  be  composed. 

The  following  loads  are  those  allowed  in  different  cities  of  the 
United  States,  in  addition  to  the  dead  load.  The  load  of  the 
structure  is  termed  the  dead  load.  The  load  imposed  on  the  floor 
by  the  materials  stored  there  is  termed  the  floor  loading  and  is 
often  spoken  of  as  the  live  load.  Strictly  speaking,  however,  a 
live  load  is  a  moving  load  and  has  double  the  effect  of  the  same 


Floor  Loads.  43 

weight  in  pounds  of  a  stationary  load.  For  example,  a  live  load 
of  200  Ibs.  per  sq.  ft.  might  be  calculated  as  if  it  were  a  steady  load 
of  400  Ibs.  for  a  bridge  but  as  200  Ibs.  in  a  building. 

Floor  loads.  Dwellings,  apartment  houses,  hotels,  tenement 
houses,  or  lodging  houses,  70  Ibs.  per  sq.  ft.;  office  buildings,  first 
floor,  150  Ibs.  per  sq.  ft.;  above  the  first  floor,  100  Ibs.;  schools 
and  places  of  instruction,  80  Ibs.;  stables  or  carriage  houses,  80 
Ibs.;  building  for  public  assembly,  150  Ibs.;  ordinary  stores,  light 
manufacturing  and  light  storage,  120  Ibs.;  stores  for  heavy  ma- 
terials, warehouses  and  factories,  150  to  250  Ibs.;  roofs,  pitch  less 
than  20  deg.,  50  Ibs. ;  pitch  more  than  20  deg.,  30  Ibs. 

Live  load  on  slabs  to  be  used  for  highway  purposes  should  be 
about  100  Ibs.  per  sq.  ft.  (equal  to  dead  load  of  200  Ibs.)  and  the 
fibre  stress  in  the  concrete  should  not  exceed  400  Ibs.  per  sq.  in. 
with  n=15.  For  spans  not  exceeding  50  feet  a  highway  bridge 
can  be  calculated  in  the  same  manner  as  given  for  floor  slabs. 
Sometimes  considerable  economy  can  be  effected  by  calculating 
two  beams  about  18  inches  thick,  to  carry  the  load,  and  using  them 
as  parapets.  The  floor  slab  across  will  be  connected  to  these  beams 
a  little  below  the  neutral  axis,  but  this,  of  course,  depends  upon  the 
head  room  required.  Such  parapets  should  have  double  reinforce- 
ment and  be  designed  that  way.  The  steel  in  the  floor  slab  should 
be  turned  up  into  the  beam  far  enough  to  provide  for  hanging  (re- 
action). Abutments  must  be  rigid  and  go  to  a  good  foundation. 
See  bulletin  No.  15,  "Concrete  Bridges,"  American  Association  of 
Portland  Cement  Manufacturers,  Land  Title  building,  Philadel- 
phia, Pa. 

Sidewalks  in  Chicago  are  calculated  for  300  Ibs.  per  sq.  ft., 
including  weight  of  slab;  in  St.  Louis  and  some  other  cities,  for 
300  Ibs.  per  sq.  ft.  in  addition  to  weight  of  slab. 


CHAPTER  III. 

\ 

COLUMNS. 

Columns  of  reinforced  concrete  are  used  because  they  cost 
less  in  place  than  columns  of  steel  or  iron.  They  are  also  used 
because  the  majority  of  men  who  design  in  reinforced  concrete  like 
to  use  as  much  of  the  material  as  possible.  To  them  it  seems  a 
profanation  to  use  a  column  of  steel  or  iron  and  have  the  walls  and 
floors  of  concrete. 

Concrete  columns  occupy  more  space  than  columns  of  other 
materials  commonly  used  for  such  purposes.  Taking  for  example 
a  load  of  fifty  tons  to  be  supported  by  a  column  18  feet  high, 
the  sizes  are  as  follows: 

Reinforced  concrete   18  x  18  inches 

White  pine  or  spruce   13  x  13  inches 

Oak    12  x  12  inches 

Yellow    pine    11  x  11  inches 

Cast  iron  (hollow  and  round) 8  in.  diameter 

Steel    (2  6-inch  latticed   channels) 6x   8  inches 

In  a  floor  having  twenty  columns  the  space  occupied  by  round 
cast  iron  columns  will  be  less  than  six  square  feet.  The  space 
occupied  by  the  same  number  of  steel  columns  will  be  less  than 
eight  feet,  while  the  space  occupied  by  the  same  number  of  rein- 
forced concrete  columns  will  be  over  forty  square  feet.  When 
space  is  rented  by  the  square  foot,  or,  rather,  the  value  of  space 
is  based  on  its  rental  value,  the  economy  of  reinforced  concrete 
columns  is  sometimes  questionable.  In  situations  where  the  space 
occupied  is  of  little  consequence  and  where  durability  is  the  chief 
thing  sought,  the  reinforced  concrete  column  has  a  place.  Even 
in  such  a  place,  it  may  not  be  as  good  as  columns  of  other  materials 
when  the  cutting  off  of  the  light  is  also  considered. 

Two  methods  are  used  for  reinforcing  columns.  In  one  all 
the  reinforcement  is  vertical.  It  is  tied  at  intervals  or  is  wrapped 
with  wire,  but  such  tying  or  wrapping  is  empirical  and  is  more 
to  keep  the  reinforcement  in  place  than  for  any  other  purpose. 
The  other  method  is  to  have  simply  enough  vertical  rods  to  tie  the 

44 


Different  Types  of  Columns  45 

wrappings  to  and  to  reinforce  by  spiral  wrappings  of  wire  or  steel 
rods. 

There  are  two  modifications  that  are  hardly  entitled  to  be 
called  reinforced  concrete,  but  should  rather  be  styled  "concrete 
protected"  columns.  In  one  the  column  must  be  of  steel  suffi- 
cient in  size  to  carry  the  load  and  with  concrete  to  protect  it  and 
add  the  necessary  stiffness  and  factor  of  safety.  In  the  other  the 
reinforcement  is  built  as  a  column  large  enough  to  carry  all  the 
dead  loads  and  the  construction  loads.  The  concrete,  when  added, 
makes  it  strong  enough  to  take  care  of  all  live  loads.  This  last 
form  is  coming  rapidly  into  use,  together  with  built-up  reinforce- 
ment for  beams.  It  admits  of  certainty  in  placing  the  reinforce- 
ment, while  at  the  same  time  lessening  the  time  occupied  in  con- 
struction. In  the  opinion  of  the  writer,  the  building  ordinances 
in  all  cities  will  gradually  insist  upon  such  construction. 

When  columns  are  reinforced  with  vertical  rods,  the  few 
experiments  made  do  not  show  results  that  are  entirely  satis- 
factory. They  do  show,  however,  that  this  method  is  good  if 
the  concrete  is  well  proportioned,  well  mixed  and  thoroughly 
compacted  when  placed.  The  steel  should  be  as  straight  as 
possible  and  rest  upon  bed  plates  at  the  bottom.  The  total  load 
should  not  exceed  350  or  500  pounds  per  square  inch. 

Generally  building  ordinances  require  that  reinforced  concrete 

columns  have  a  ratio  not  exceeding —r-  =  12.    In  other  words, 

the  least  thickness  or  diameter  will  be  in  inches  equal  to  the 
clear  height  in  feet.  It  is  plain  that,  as  the  steel  rods  carry 
part  of  the  load,  they  might  bend  enough  to  destroy  the  con- 
crete. In  a  long  column,  flexure  might  be  caused  by  a  heavy 
load,  although  in  the  tests  made  up  to  date  no  bending  seemed 
to  have  been  developed  in  columns  having  a  ratio  of  less  than 
25.  Some  designers  use  a  ratio  of  20  with  c  =  350  and  a  ratio 
of  12  with  c  =  500. 

Columns  reinforced  by  spiral  wrappings  can  be  loaded  up  to 
about  1,000  pounds  per  square  inch,  because  the  concrete  is  en- 
cased in  the  wrappings  as  in  a  steel  cylinder.  As  the  load  comes 
upon  it  the  tendency  is  to  bulge  outward.  This,  being  resisted 
by  the  spirals,  enables  greater  strength  to  be  developed  than  by 
the  use  of  longitudinal  bars  or  rods  alone. 

A  spirally  wound  column  is  not  very  stiff,  and  if  such  rein- 
forcement is  used  in  long  columns  it  must  be  assisted  by  longi- 
tudinal rods.  The  place  for  these  rods,  of  course,  is  inside  the 


46  Reinforced  Concrete. 

spiral.  One  objection  to  the  use  of  spirally  reinforced  columns 
is  that  there  must  be  some  settlement  before  the  bulging  is  suffi- 
cient to  call  into  play  the  strength  in  the  spirals.  Within  a  fibre 
stress  of  1,000  pounds  per  square  inch,  if  the  column  is  well 
made,  this  need  not  cause  anxiety.  The  writer,  however,  prefers 
to  use  lower  stresses  and  longitudinal  reinforcement 

Recent  experiments  seem  to  indicate  that  when  vertical  rods 
are  used  in  spirally  wound  columns  they  are  an  element  of 
danger.  As  already  stated,  the  ultimate  strength  of  the  column 
is  increased,  but  there  is  nothing  gained  when  loads  are  light, 
as  they  are  generally.  That  is,  if  the  steel  is  used  in  the  form 
of  spiral  wrappings  it  will  generally  be  found  to  be  expensive 
reinforcement  unless  high  stresses  are  used.  When  some  of  it 
is  in  the  form  of  longitudinal  rods  and  the  stress  is  so  high 
that  the  column  settles  enough  to  call  the  spiral  wrapping  into 
service,  then  the  steel  is  apt  to  be  stripped  from  the  longi- 
tudinal rods,  thereby  dividing  the  body  of  the  column.  When 
this  is  done  and  each  rod  is  free  to  act  alone,  it  buckles  and  the 
column  is  rapidly  destroyed.  Therefore  when  a  column  is 
wound  there  should  be  as  little  vertical  steel  as  possible. 

A  volume  of  steel  in  the  form  of  a  large  wire  or  small  round 
rods  wrapped  spirally  has  2.4  times  the  effect  that  the  same 
volume  of  steel  would  have  if  disposed  in  vertical  reinforcement. 
That  is,  provided  it  is  wrapped  with  a  pitch  of  from  one-sixth 
to  one-seventh  the  diameter. 

A  knowledge  of  this  fact  permits  one  of  two  alternatives.  The 
column  size  may  be  retained  and  a  smaller  amount  of  steel  used 
than  if  vertical  reinforcement  is  adopted,  or  the  size  of  the  column 
may  be  reduced  by  using  a  stress  in  the  concrete  2.4  times  greater 
than  the  stress  ordinarily  considered  safe.  This  means  that  we 
can  use  in  a  spirally  wound  column  a  stress  of  840  pounds  per 
square  inch  instead  of  the  350  pounds  used  in  a  vertically  rein- 
forced column,  or  we  may  use  1,200  pounds  per  square  inch  instead 
of  500  pounds.  The  placing  of  vertical  reinforcement  is  cheaper 
and  it  is  easier  to  get  the  reinforcement  right  than  to  wind  the 
steel.  Compilers  of  conservative  building  ordinances  so  far  do 
not  look  kindly  upon  spirally  wound  columns  except  when  they  are 
fabricated  in  shops  and  brought  to  the  building.  Neither  do  they 
like  high  stresses. 

The  tables  of  column  divisors  are  used  as  follows:     Assume 

a  value  of  --  and  thus  get  the  area  of  the  cross  section  of  the 


Percentage  of  Steel. 


47 


column.  Perhaps  the  building  ordinance  fixes  this  ratio,  in  which 
case  use  it  and  obtain  the  area.  Divide  the  weight  in  pounds  to 
be  carried  by  the  column  by  the  area.  Under  the  value  of  "n" 
fixed  by  the  ordinance,  find  the  column  divisor.  On  the  same 
horizontal  line  will  be  found  the  percentage  of  steel. 

If  a  certain  percentage  of  steel  is  assumed  and  a  value  of  "n" 
selected,  the  column  divisor  in  the  "n"  column  on  the  same  line 
as  the  steel  percentage  will  be  used  as  a  divisor  of  the  weight  in 
pounds.  The  result  will  be  the  area  of  the  column  in  square  inches. 

The  tables,  as  may  be  seen,  have  been  calculated  with  c  =  350 
and  =500  pounds  per  square  inch,  with  values  of  "n"  ranging 
from  8  to  20  and  with  from  1  to  10  per  cent  of  steel. 

TABLES  OF  COLUMN  DIVISORS 
for  longitudinally  reinforced-concrete  columns. 


Table  VII.     c  =  350  Ibs.  per  sq.  in. 

Per  cent 
of  steel 

n=       8 

10 

12          |           15 

20 

f  =  2800 

3500 

4200        |         5250 

7000 

—DIVISORS— 

1 
2 
3 
4 
5 
6 
10 

374.5 
399 
423.5 

448 
472.5 
497 
595 

381.5 
413 
444.5 
476 
507.5 
539 
665 

388.5 
427 
465.5 
504 
542.5 
581 
735 

399 
448 
497 
546 
595 
644 
840 

416.3 
483 
549.5 
616 
682.5 
749 
1015 

Table  VIII.     c  =  500  Ibs.  per  sq^in. 

Per  cent 
of  steel 

n=       8 

10           |           12           |           15 

20 

f  =  4000 

5000 

6000        |          7500        |         10000 

—DIVISORS— 

1 
2 
3 
4 
5 
6 
10 

535 
570 
605 
640 

675 
710 
850 

545 
590 
635 
680 
725 
770 
950 

555 
610 
665 
720 
775 
830 
1050 

570 
640 
710 
780 
850 
920 
1200 

595 
690 
785 
880 
975 
1070 
1450 

While  the  percentages  of  steel  are  given  as  though  no  limit 
is  considered,  there  is  a  practical  limit  depending  on  the  cost 
of  the  steel  and  the  ease  of  getting  it  in  the  form  of  rods  and 
bars  as  compared  with  getting  structural  shapes  and  using  con- 
crete protected  columns  instead  of  reinforced  concrete  columns. 
The  heavy  lines  are  drawn  where  the  same  amount  of  steel  in 
a  steel  column  would  carry  the  entire  load  without  the  concrete. 


48  Reinforced  Concrete. 

The  tables  were  calculated  by  the  following  formula: 

P  =  c  (Ac-f-nA8),  in  which 

P  =  total  load  in  pounds  or  compressive  strength  of  section. 

c  =  compressive  load  per  square  inch  permitted  on  concrete. 

^=aareeaao°ffc±ete     |  -  cross  section. 

n  =  ratio  of  moduli  of  elasticity. 

To  understand  and  use  this  formula,  assume  a  unit  value  for 
steel  and  concrete,  when  it  becomes 

P  =  c  (1-r-nl), 

and  by  multiplying  the  quantities  in  the  parenthesis  by  an  assumed 
value  of  c  (for  example,  350)  and  of  n  (for  example,  12),  we 
have 

P  =  350  (1  +  12  (1)  )  =350  +  12X350. 

The  following  example  illustrates  the  method  of  calculation, 
taking  the  values  already  assigned  and  starting  with  a  1  per  cent 
reinforcement  of  steel: 

350  X  12  X  0.01  (the  per  cent  of  steel) =  42.0 

350  X  0.99  (the  per  cent  of  concrete) =  346.5 

Column  divisor 388.5 

The  total  load  in  pounds  diivded  by  388.5  will  give  the  area 
in  square  inches  of  the  column  section  for  a  reinforcement  of  1 
per  cent  of  steel,  when  "c"  is  350  and  "n"  is  12. 

The  factor  "n"  is  very  important  in  column  formulas.  Pro- 
fessor Talbot  says  it  is  apt  to  be  misleading  to  use  it,  and  to  term 
it  the  ratio  between  the  moduli  of  elasticity  is  indefinite  and  un- 
desirable. He  therefore  uses  a  formula  having  a  different  ratio, 
as  follows: 

P  =  Ac(l+(n  — l)p),  in  which 

P  =  total  load  in  pounds  or  compressive  strength  of  section. 

A  =  total  area  of  section  (including  concrete  and  steel)  in 
square  inches. 

c  =  compressive  load  per  square  inch  allowed  on  the  concrete. 

n  =  ratio  of  stress  in  steel  to  stress  in  concrete. 

p  =  percentage  of  steel  or  ratio  which  area  of  steel  bears  to 
the  area  of  the  concrete. 

The  tables  of  column  divisors  obtained  by  the  first  formula 
were  checked  by  the  second. 

The  ratio  of  the  moduli  of  elasticity  has  been  considered  of 
great  importance  in  column  design,  assuming  the  adhesion  or 
bond  between  steel  and  concrete  to  be  sufficient.  When  a  load 


Loads  on  Columns.  49 

comes  upon  the  column,  part  is  supposed  to  be  taken  by  the  con- 
crete and  part  by  the  steel.  Each  must,  therefore,  be  compressed 
precisely  in  the  ratio  of  the  relative  extensibility.  If  they  do  not, 
then  the  adhesion  will  be  destroyed,  after  which  each  material  will 
act  independently,  making  certain  the  destruction  of  the  column. 
When  the  adhesion  is  destroyed,  each  rod  becomes  a  long  and 
extremely  slender  column. 

To  call  "n"  the  ratio  between  the  moduli  of  elasticity  is  not 
correct.  The  term  "ratio  of  stress  in  steel  to  stress  in  concrete" 
gives  a  clearer  idea.  The  ratio  is  sometimes  as  high  as  20,  but 
the  safest  value  to  use  when  a  factor  of  safety  of  from  4  to  5  is 
wanted  in  the  concrete,  lies  between  12  and  15. 

Calling  A  the  total  area  of  the  column  section  (including  the 
steel)  and  "p"  the  percentage  of  reinforcement,  the  area  of  the 
steel  will  be 

PA 
the  unit  stress  in  the  steel  will  be 

nc 
and  the  area  of  the  concrete  will  be 

A  (1-p) 
The  total  compressive  stress  in  the  steel  will  be 

pAnc 
and  in  the  concrete  will  be 

Ac  (1-p) 

How  much  strength  does  the  longitudinal  steel  add  to  the 
concrete?  The  formula: 

P  =  Ac(l-{-(n  —  l)p) 

indicates  that  each  addition  of  1  per  cent  of  steel  adds  (n — 1)  % 
of  strength  to  the  concrete. 

The  same  formula  enables  lis  to  find  when  the  steel  in  the. 

usual  structural  shapes  will  carry  the  load  without  the  concrete. 

Let  s  =  the  ordinary  stress  used  in  steel  columns.    Usually 

16,000  pounds  per  square  inch. 
A' =  area  of  steel  in  steel  column  (cross  section). 
pA  =  area   of   steel   reinforcement    in   reinforced    concrete 
column 

Then  Ac  (1  +  (n  —  1)  p)  =  sA' 
pA  =  sA' 

P=f_c(n  — 1) 
That   is,   the   safe   fibre   stress   allowed   in   the   concrete   is 


50  Reinforced  Concrete. 

divided  by  the  usual  fibre  stress  in  steel  structural  work  minus 
the  safe  concrete  stress  multiplied  by  (n  — 1),  to  get  the  per- 
centage of  steel  that  will  carry  the  load  without  the  concrete, 
provided  it  is  in  the  usual  structural  form. 

It  is  then  simply  a  question  of  the  balancing  of  costs.  If 
the  concrete  column  containing  reinforcement  can  be  built  at 
less  cost,  or  if  the  steel  can  be  obtained  in  the  form  of  rods  and 
bars  within  less  time  than  it  can  be  obtained  in  shapes  that  can 
be  worked  into  the  usual  form  of  steel  column,  then  the  rein- 
forced column  may  be  best. 

The  steel  should  be  so  disposed  in  the  column  that  it  will  be 
protected  by  at  least  one  inch  of  concrete,  and  so  the  concrete 
can  flow  readily  between  the  bars.  Large  bars  should  be  used 
in  preference  to  small.  They  may  be  so  placed  that  the  column 
may  be  square,  round  or  octagonal  in  section.  The  writer  believes 
it  is  well  to  allow  a  part  of  the  area  for  fire  protection  of  the 
steel.  In  the  examples  given  at  the  beginning  of  this  chapter 
the  area  of  a  reinforced  concrete  column  is  given  at  18"  x  18"  = 
324  square  inches.  Using  the  tables  above,  the  exact  dimension 
will  be  found  nearer  16  inches  square,  and  the  additional  size  is 
given  for  the  thorough  protection  of  the  column. 

In  this  connection  it  may  be  stated  that  the  logical  position 
for  the  steel  is  in  the  center  of  the  column,  but  it  should  be 
nearer  the  outside,  because  the  concrete  should  be  in  as  large  a 
body  as  possible  and  be  not  too  much  cut  up.  The  writer  believes 
that  the  body  of  concrete  inside  the  steel  should  make  a  column 

of  clear  concrete  having  a  ratio  of  — r-  equal  to  three-fourths  the 

*-atio  of  the  whole  column.  That  is,  if  calculations  show  the 
coitJmn  should  be  16  inches  square,  the  steel  can  be  arranged  to  fit 
inside  a  12-inch  square.  This  rule  is  wholly  empirical,  and  by 
some  designers  may  not  be  considered  good.  It  should  not  be 
adhered  to  if  it  results  in  an  interior  section  of  less  than  8x8 
inches,  and  does  not  need  to  be  followed  closely  if  a  larger  inside 
square  can  be  obtained  for  the  steel  and  still  leave  a  thickness 
of  at  least  one  inch  of  concrete  protection.  In  columns  liable  to 
exposure  to  fire  it  will  be  a  safe  precaution  to  increase  the  dimen- 
sions of  the  column  by  at  least  2  inches. 

When  the  reinforcement  calls  for  four  large  bars,  a  good 
plan  is  to  use  four  angles  of  equivalent  area  and  make  of  them  a 
latticed  column.  Otherwise  use  square  bars  wrapped  with  No.  8 
or  No.  10  plain  wire,  tying  it  with  No.  16  or  No.  18  wire  at  each 


Distribution  of  Steel.  51 

intersection,  merely  to  preserve  the  pitch,  which  should  be  equal 
to  half  the  thickness  or  diameter.  The  wrapping  should  be  com- 
menced at  one  corner  and  go  around  in  as  long  strands  as  possible. 
When  spliced,  it  should  be  by  hooking  the  ends  and  making  long 
twisted  joints.  Four  rods  generally  suffice,  except  when  their  size 
would  render  them  difficult  to  handle,  when  a  larger  number  of 
smaller  rods  can  be  used. 

Owing  to  the  shrinkage  stresses  developed  in  concrete,  which 
may  stress  the  steel  unduly  before  the  load  comes  on  the  column, 
it  is  good  practice  to  use  plain  bars  or  rods  in  columns  and  pour 
about  five  diameters  in  height  at  a  time,  leaving  an  interval  of 
about  two  or  three  hours  between  pourings.  The  columns  should 
be  completed  before  the  pouring  is  commenced  for  the  floors  and 
beams  they  support.  Concrete  in  columns  usually  settles  consider- 
ably in  setting,  and  for  this  reason  it  is  well  to  allow  about  three 
or  four  hours'  time  to  elapse  before  pouring  the  beams  connecting 
to  the  top  of  the  columns. 

This  rule  for  pouring  columns  does  not  always  work  well, 
for  some  engineers  have  told  the  writer  that  they  noticed  small 
cracks  that  appeared  in  the  concrete  below  when  it  was  set  rather 
hard  but  not  quite  hard  enough  to  bear  the  weight  of  the  fresher 
concrete  poured  above.  It  is  quite  likely  they  waited  too  long 
between  pourings.  The  idea  of  having  a  little  time  elapse  is  to 
permit  of  thorough  settlement  in  small  masses  and  to  allow  a 
somewhat  uniform  setting  thereby. 

When  vertical  rods  used  in  columns  are  shorter  than  the  col- 
umn, pieces  put  on  to  lengthen  them  should  rest  on  top  instead  of 
being  wired  side  by  side,  and  the  joint  should  be  made  in  a  sleeve 
of  pipe  just  fitting  the  steel.  Alongside  each  joint  and  about 
four  times  as  long  as  the  sleeves,  which  should  be  twenty-four 
diameters  long,  should  be  set  a  half-inch  bar  as  a  joint  stiffener. 
It  should  not  be  wired  to  the  column  reinforcement,  but  should  be 
a  separate  piece,  entirely  surrounded  by  concrete. 

Mr.  W.  A.  Hoyt,  C.  E.,  structural  engineer  with  the  Corn 
Products  Company,  informs  the  writer  that  he  does  not  set  his 
vertical  rods  until  ready  to  go  on  with  the  columns.  It  often 
happens  in  construction  work  that  the  column  footings  are  com- 
pleted long  before  the  columns  are  poured.  The  long  steel  rods 
are  a  problem  to  handle.  Some  men  place  in  the  footings  short 
s'ections  of  pipe  and  set  the  steel  in  the  pipe  when  ready  to  go 
up  with  the  work.  In  spite  of  all  care,  more  or  less  dirt  will 
collect  in  the  pipes.  Mr.  Hoyt  uses  instead  short  sections  of 
steel  which  project  a  foot  or  two  above  the  footing.  When 
ready  to  go  ahead  a  sleeve  is  placed  around  them  and  the  ver- 
tical rods  are  set  in  this  sleeve. 


CHAPTER  IV. 
WALLS,  TANKS  AND  FOOTINGS. 

Retaining  walls  fail  by  sliding  forward,  by  overturning,  or 
by  breaking  across  at  a  point  approximately  one-third  of  the 
height  up  from  the  bottom. 

Until  the  advent  of  reinforced  concrete  all  walls  were  de- 
signed to  have  enough  bulk  to  prevent  failing  by  any  of  the 
above  ways.  It  was  realized  that  if  masonry  could  be  made 
with  enough  cohesion  to  stand  bending,  walls  could  be  sunk 
far  enough  in  the  earth  so  they  would  not  slide  forward;  that 
they  could  be  anchored  in  some  way  to  prevent  overturning,  but 
that  all  this  involved  the  production  of  strains  that  would  cause 
the  wall  to  break.  Therefore,  the  strong  masonry  was  needed. 
This  is  apart  from  the  fight  between  the  men  who  designed  walls 
by  theoretical  formulas  and  those  who  stood  faithfully  by  empir- 
ical formulas,  or,  as  some  called  them,  "rule-of-thumb  methods." 
There  was  never  any  reason  for  the  latter  fight,  for  walls 
that  were  designed  according  to  theory,  coupled  with  judgment, 
always  stood.  It  was  when  a  man's  passion  for  pure  theoretical 
reasoning  overcame  his  better  judgment  that  walls  fell,  except 
in  the  very  few  exceptional  cases  where  the  circumstances  were 
such  that  even  walls  designed  by  empirical  rules,  supposed  to 
embody  the  best  judgment  in  exceptional  cases,  would  have 
failed.  Empirical  rules  simply  set  a  thickness  for  a  wall  accord- 
ing to  the  height  and  practically  independent  of  the  character  of 
the  backing,  except  when  a  man  liked  to  add  a  guess  of  his  own. 
When  walls  commenced  to  be  built  of  reinforced  concrete  all 
the  carefully  treasured  empirical  rules  as  to  weight  and  thickness 
of  walls  had  to  go ;  for  whereas  in  the  case  of  bulk  the  pressure 
was  of  little  or  no  moment,  so  long  as  certain  procedures  were 
adhered  to,  when  it  came  to  the  designing  of  a  wall  in  which  the 
minimum  of  material  was  the  goal,  pressures  had  to  be  taken 
into  account.  Reinforced  concrete  walls  are  in  shape  like  a  cap- 
ital letter  L  or  like  an  inverted  capital  T.  The  weight  of  the 
wall  is  small  and  the  weight  of  the  backing  upon  the  rear  leg 
has  to  be  taken  into  consideration.  Therefore,  bending  moments 

52 


Retaining  Walls.  53 

develop  which  cannot  be  withstood  in  old  style  masonry  hav- 
ing joints,  so  are  taken  care  of  by  the  reinforcement. 

Considering  a  vertical   strip   12"   wide  on  a  wall  the  total 
pressure  is  found  by  the  formula: 

P  =  y  X  d2 

in  which  d  is  the  depth  in  feet  from  the  top  of  the  wall  to  the 
point  at  which  the  pressure  is  wanted,  and  the  material  is  no 
higher  than  the  wall. 

The  following  table  gives  values  of  y  for  different  materials: 

TABLE  IX. 

Water y  =  31.25 

Fine  dry  sand y  =  15.7 

Dry  loose  gravel y  =  12.1 

Dry  loose  earth y  =    8.8 

Moist  earth  y  —    5.6 

Dense,  natural  earth y  =    6.2 

Considering  a  horizontal  strip  12"  wide;  at  any  depth  the 
pressure,  w  (or  load),  per  square  foot,  is  as  follows. 

w  =  2y  X  d 

A  surcharged  wall  is  one  that  supports  a  sloping  fill.     The 
pressure  on  any  foot  will  be 

and  the  total  pressure  will  be 

P  =  1.5y  X  d2 

The  depth  is  the  depth  from  the  top 
of  the  wall  as  already  explained,  and 
while  the  formula  is  not  exact,  it  is 
close  enough  for  all  practical  pur- 
poses. 

Reinforced  concrete  retaining  walls 
may    be    designed    as    cantilevers,    in 
which  case  the  formula  for  P  is  used,          f~7 
or  they  may  be  designed  with  coun-          * **  rt 

terforts,   in   which   case   the   formula 

for  w  is  also  used.  Fig.  7  represents  a  wall  which  is  a  compromise 
between  the  L  and  the  inverted  T.  In  order  that  the  system  of  let- 
tering used  may  apply  to  both  designs,  DC  or  El  represent  the 
height,  which  will  hereafter  be  designated  by  h.  The  pressure  P 


54  Reinforced  Concrete. 

is  applied  at  h/3,  to  obtain  the  bending  moment  at  CI,  which  will 
determine  the  thickness  at  that  point.  The  pressure  is  applied  at  a 
point  one-third  the  height  for  the  reason  that  the  area  of  pres- 
sure is  a  triangle  and  forces  act  always  through  the  center  of 
gravity  of  bodies ;  the  center  of  gravity  of  a  triangle  being  one- 
third  up  from  the  base. 


'2 

?  k 

o 

1 

h 

a 

0 

. 

if 

u 

a  CD 

o 

4  a 

u 

:> 

J)      a  ^ 

5 

0 

§ 

X8 

W3 

V 

8^^^QPP 

<V>«t««#M>V\WI 

b 

vV 

i-4""~j 

FIG.  8 — Two  TYPES  OF  RETAINING  WALLS. 


Two  calculations  will  always  be  made  to  obtain  the  economic 
design.  The  first  calculation  will  not  take  the  weight  of  the 
wall  into  account,  and  the  base  AH  will  be  taken  at  a  length 
equal  to  h/2.  The  area  DFHK  in  square  feet,  multiplied  by  100 
Ibs.,  the  weight  of  one  cubic  foot  of  earth,  will  be  taken  as  the 
weight  of  the  wall  to  resist  the  pressure,  P.  Find  the  center  of 
gravity  and  through  it  vertically  pass  a  line  to  represent  to  scale 
the  weight  just  found.  Through  it  horizontally  pass  a  line  to 
scale  representing  the  pressure.  Complete  the  parallelogram  and 
draw  the  resultant.  The  position  of  this  resultant  is  of  import- 
ance, for  in  order  that  the  maximum  pressure  on  the  base  be 
not  greater  than  twice  the  average,  and  that  there  be  no  ten- 
sion on  the  back  side  of  the  foundation,  the  distance  from  the 


QF    1  ttt  -x 

UNIVERSITY   I 

OF  / 

Retaining  Walls.  55 

resultant  to  the  middle  point  of  the  base  must  not  exceed  1/6 
the  base. 

To  find  pressure  on  base: 

Let  F  =  pressure  on  base  in  pounds  per  sq.  ft.  at  A. 

Let  W  =  weight  in  pounds  of  the  wall  and  backing    (area 

DFHK). 
Let  b  =  length  of  base,  AH. 

d  =  distance  in  feet  from  point  of  intersection  of  result- 
ant with  bottom  of  base,  to  the  nearest  extremity  of  the 
base. 

2W 
Then  F  =    ^  ,  when  d  is  equal  to  or  less  than  b/3. 

4W 
And    F  —     ^2  (b  —  1.5d),    when    d    is    equal    to    or    greater 

than  b/3. 
Or  the  following  general  formula  can  be  used: 

*  =fer> 

This  pressure,  F,  on  the  base  is  the  maximum  pressure  which 
it  is  estimated  can  be  borne  by  the  earth  on  which  the  wall  is 
built.  If  the  foundation  will  not  stand  such  a  pressure  the  base 
may  be  lengthened  or  piles  can  be  driven  under  the  toe,  AB. 

The  bending  moment  at   CK  will  be  practically  equal   to 

=  ^-XBCX-55BC;  when  EC=—^- ,  or  for  shorter  toe 

BC       \ 

^FjxBCX-eBC 

W  X  IG 
The  bending  moment  at  IJ  is,  M  = ^ — 

As  the  pressure  against  the  wall  is  at  right  angle  to  the  sur- 
face pressed,  it  brings  the  resultant  a  little  nearer  the  center  if  the 
pressed  surface  is  sloping  instead  of  vertical.  This  increases  the 
stability  and  decreases  the  bending  moment  in  the  case  of  water, 
but  makes  practically  no  difference  for  earth. 

The  dotted  lines  indicate  how  the  steel  will  be  placed  to  take 
care  of  the  bending  moments  developed.  As  the  shearing  stress 
on  CK  will  be  great  the  thickness  should  be  made  double 

T  (~* 

what  the  bending  moment  would   demand,   when  BC  <  -r- 

o 

thus  using  the  calculation  for  bending  moment  simply  to  obtain 
the  steel  area.  The  thickness  at  IJ  should  be  sufficient  to  develop 
the  bond  strength  of  the  steel  rods  in  the  wall.  Before  determin- 


( 
F"~ 


56  Reinforced  Concrete. 

ing  this,  however,  the  thickness,  1C,  should  be  obtained,  and  the 
thickness  of  the  wall  at  regular  intervals,  in  order  to  obtain  the 
correct  shape,  which  will  approximate  a  curve.  Three  points 
should  be  enough,  and  they  may  be  connected  by  straight  lines, 
the  front  of  the  wall  being  vertical,  or  if  desired  may  have  a 
slight  batter.  The  last  slope  of  the  back  towards  the  bottom 
may  be  such  that  the  steel  parallel  with  it  may  extend  into  the 
base  far  enough  to  develop  bond,  or  at  its  connection  with  the 
base  the  angle  may  be  divided  and  the  steel  given  a  different 
slope  in  order  to  secure  length  of  embedment  without  unduly 
thickening  the  base. 

The  thickness,  IJ,  will  be  used  to  determine  the  amount  of 
steel,  but  the  actual  thickness,  as  seen,  depends  upon  the  bond 
embedment  of  the  steel  in  the  wall.  All  the  steel  must  be  run 
far  enough  past  the  points  of  maximum  moment  to  develop  suf- 
ficient bond.  (See  Table  V,  Chapter  I.). 

The  steel  in  the  base  will  run  from  the  front  to  the  back 
(perpendicular  to  the  length  of  the  wall),  and  the  steel  in  the 
wall  will  be  vertical.  All  of  it  need  not  run  to  the  top  of  the 
wall,  but  it  may  be  reduced  as  shown  by  the  calculations  for 
bending  moment.  Longitudinal  rods  should  be  placed  in  the 
wall  and  in  the  base  at  regular  intervals  to  take  care  of  tem- 
perature stresses  and  to  assist  in  preserving  the  intervals  be- 
tween the  main  reinforcing  rods.  The  steel  should  be  well  wired 
together  at  all  intersections. 

Before  figuring  the  steel,  however,  a  second  calculation 
should  be  made  after  the  dimensions  of  the  wall  have  been  fixed 
as  shown.  The  wall  should  be  drawn  to  scale  and  a  new  center 
of  gravity  found,  representing  the  compound  section  made  up 
of  the  wall  weighing  150  Ibs.  per  cu.  ft.  and  the  earth  filling  on 
the  slab  weighing  100  Ibs.  per  cu.  ft.  To  allow  of  some  reduc- 
tion in  size  it  may  be  best  to  use  120  Ibs.  for  the  concrete  por- 
tion. With  this  calculation,  which  may  result  in  some  changes 
being  made  in  sizes,  the  work  can  stop  and  the  steel  be  calcu- 
lated for  the  wall.  The  longitudinal  steel  should  be  equal  to 
about  one-third  of  one  per  cent  in  area  of  cross  section.  The 
edges,  BA,  GH  and  DE  may  be  of  any  thickness  sufficient  to 
give  adequate  protection  to  the  steel,  the  slope  being  gradual 
and  thus  effecting  some  saving  in  material. 

As  walls  designed  in  this  manner  are  more  apt  to  be  heaved 
by  frost  than  the  usual  type  of  gravity  wall,  the  bottom  slab 
must  be  placed  deep  enough  to  avoid  any  danger  of  frost  ac- 


Retaining  Watts.  57 

tion,  but  as  this  is  a  case  where  moments  enter  in  the  following 
formula  may  be  used,  in  which  f  =  depth  below  surface  in  feet. 

f  =  .0007  F,  which  gives  a  minimum  value  for  the  depth. 

Reinforced  concrete  walls  are  often  designed  with  counter- 
forts back  of  them,  tieing  the  face  slab  to  the  bottom  slab  in  the 
rear.  This  is  a  simple  wall  to  figure  and  easy  to  build,  but  on 
account  of  more  form  work,  by  reason  of  the  counterforts,  may 
be  more  expensive  at  times  than  the  cantilever  wall,  although 
generally  requiring  less  material. 

First  determine  the  spacing  between  the  counterforts.  Then 
design  the  vertical  wall  as  a  slab  between  the  counterforts,  with 
horizontal  reinforcement.  Calling  the  distance  between  counter- 
forts, in  inches,  L;  the  bending  moment  on  each  horizontal  strip 
12"  wide  will  be: 


in  which  w  =  2y  X  d  (load  per  sq.  ft.  at  depth,  d.) 

The  total  load  on  any  horizontal  strip  will  be  wL,  and  one- 
half  of  this  at  each  end  is  reaction,  thus  indicating  how  far  the 
steel  must  run  back  into  the  counterfort  for  bond.  In  addition 
to  this  horizontal  reinforcing  steel  there  should  be  vertical  steel 
of  approximately  one-third  of  one  per  cent  area  used  to  space 
the  horizontal  rods  and  going  to  the  top  of  the  wall.  At  the 
bottom  it  should  turn  gradually  into  the  slab  at  the  back,  going 
into  it  to  help  tie  the  face  and  base  together. 

The  rear  slab  may  be  lifted  by  the  tendency  of  the  wall  to 
overturn  because  of  the  pressure.  In  this  case  w  is  equal  to  the 
weight  of  a  column  of  earth  12"  square,  with  a  height=h,  at  the 
back  edge  of  the  slab,  but  is  zero  at  the  wall.  Using  then  this 
value  for  w,  which  is  different  for  each  12"  strip  parallel  with  the 
wall, 


for  each  strip,  thus  the  reinforcement  will  be  spaced  at  greater 
intervals  nearer  the  wall  and  the  slab  should  really  be  thinner. 
The  thickness,  however,  is  maintained  for  the  benefit  of  the  weight 
given  and  to  furnish  bond  for  the  vertical  rods  and  the  rods  from 
the  toe.  The  total  load  on  each  parallel  strip  is  wL,  and  one-half 
of  this  at  each  end  is  reaction,  showing  how  far  the  steel  must 
project  up  into  the  counterfort  for  bond. 

The  counterfort  will  have  a  width  at  the  bottom  equal  to 
the  base  and  at  the  top  will  run  to  the  wall  or  may  end  in  a 
beam  along  the  top  of  the  wall.  Its  thickness  will  depend  almost 


58  Reinforced  Concrete. 

wholly  on  the  thickness  required  to  protect  the  rods  embedded 
in  it.  It  is  calculated  as  a  cantilever  having  a  load  =  PL  and 

the  bending  moment  at  the  bottom  is,  M  =  — ^ — .  With  this 
value  of  M,  calculate  the  steel  required  and  make  the  counterfort 
wide  enough  to  take  it.  This  steel  will  run  along  the  back  edge 
of  the  counterfort  and  into  the  top  of  the  wall,  where  it  must 

PL 

be  embedded  for  bond  to  take  up      ^    .       At  the  bottom  the 

steel  must  be  bent  back  into  the  base  for  anchorage  and  be  em- 

2  PL 
bedded  so  it  will  stand  a  pull=: — g— . 

Usually  it  will  be  found  that  the  comparative  cost  of  plain 
and  reinforced  concrete  retaining  walls  depends  so  largely  upon 
local  costs  of  materials  and  labor  that,  for  heights  less  than  six- 
teen feet  the  plain  wall  may  be  far  cheaper.  This  is  owing  to 
the  generally  wider  base  of  the  reinforced  wall  which  calls  for 
more  excavation,  the  cost  of  form  work  and  of  the  steel  and 
labor  in  placing  steel,  and  extra  labor  involved  in  pouring  thin 
walls. 

For  comparison  use  for  the  plain  wall  the  common  rule  that 
the  breadth  of  base  will  be  one-third  the  height.  With  the  grav- 
ity wall,  the  strength  being  in  the  weight  and  solidity,  a  very 
much  cheaper  concrete  can  be  used  than  for  a  reinforced  wall. 
Comparative  estimates  should  be  always  made  before  deciding 
upon  the  type  of  wall,  remembering  also  that  with  a  gravity  wall 
not  reinforced,  the  liability  of  error  in  the  computations  is  rela- 
tively small. 

Restrained  Walls. 

Some  walls  are  designed  as  restrained  at  the  ends,  of  which 
an  example  was  given  above  in  designing  the  slabs  between 
counterforts.  Occasionally,  however,  a  wall  is  designed  that  is 
restrained  at  the  top  and  bottom,  as,  for  example,  foundation 
walls  around  basements,  pressing  against  the  basement  floor  and 
'first  floor,  and  tanks  having  floors  and  roofs  into  which  to  tie 
the  walls. 

In  such  cases  P  is  found  as  before.    The  reaction  at  the  top 

P  2P 

is  — g-  and  at  the  bottom  is  ~~3~~>  thus  showing  how  far  the  steel 

must  run  into  the  slabs,  or  beams,  to  which  the  wall  is  con- 
nected, for  bond,  or  the  pressure  which  a  basement  wall  will  ex- 
ert against  the  floors  at  its  top  and  bottom. 

If  the  wall  is  connected  to  slabs  at  top  and  bottom,  the  rein- 
forcement in  those  slabs  must  run  into  the  wall  far  enough  for 


Retaining  Watts.  59 

bond,  in  addition  to  the  wall  reinforcement  running  into  them. 
The  steel,  however,  that  ties  the  slabs  to  the  wall  must  be  in 
addition  to  the  steel  required  in  the  slabs,  as  it  is  sufficiently 
stressed,  by  reason  of  it  being  reinforcement.  Some  designers 
do  use  the  reinforcement  steel  for  tying  the  walls,  but  when  this 
is  done  it  is  dangerous. 

Sometimes  instead  of  a  slab  at  the  top,  the  tank  is  open 
and  a  beam  is  run  along  the  upper  edge,  being  designed  for  a 

P 

uniformly  distributed  load=  -g-.  This  gives  a  finish  as  a  cop- 
ing, the  span  of  the  beam  being  from  one  end  of  the  tank  to  the 
other,  or  sometimes  being  designed  as  a  continuous  beam  with 
intermediate  supports  determined  by  steel  rods  running  to  the 
opposite  side,  or  by  counterforts. 

Sometimes  the  thickness  of  the  tank  wall  is  determined  in 
advance  and  the  reinforcement  is  horizontal.  At  intervals,  de- 
termined by  the  strength  of  this  wall,  are  run  vertical  beams, 
projecting  each  side  of  the  wall,  as  pilasters.  The  strength  of 
the  vertical  beams  being  ascertained,  the  resisting  moment  of  the 
beam  is  equated  to  P  for  different  lengths  and  at  the  points  thus 
fixed  steel  rods  will  be  used  to  tie  the  opposite  sides  of  the 
tank  together  through  these  beams. 

In  a  wall  restrained  at  top  and  bottom,  the  maximum  stress 

•pi 

is  0.853h  from  the  top,  and,  M  =   „  g 

For  a  12"  vertical  strip  on  a  wall  designed  to  resist  water 
pressure, 

M  =  4h*  in  inch  Ibs.,  when  h  is  in  inches. 

The  wall  will  be  of  uniform  thickness  from  top  to  bottom, 
the  reinforcement  being  vertical  with  the  usual  horizontal  bear- 
ing steel. 

Circular  Tanks. 

For  circular  tanks  the  steel  resists  all  the  tension  and  the 
concrete  serves  only  to  protect  the  steel.  The  mixture  should 
be  fairly  rich  and  well  mixed  so  it  will  be  dense  and  water  tight. 
All  the  rods  should  be  bent  to  circles  and  ends  firmly  fastened  to- 
gether. They  should  be  either  in  the  center  of  the  concrete,  or 
not  to  exceed  twice  the  thickness  of  the  steel  from  the  outer  face. 

The  pressure,  w,  on  the  side  is  the  same  as  for  the  pressure 
against  a  vertical  wall.  The  tension  in  the  sides,  to  be  taken  by 

wD 
the  steel  is,  T  =  — — ,  in  which  w  represents  the  unit  load,  or 


60 


Reinforced  Concrete. 


FIG.   9 — REINFORCED  CONCRETE  CHIMNEY. 


Circular  Tanks.  61 

pressure  per  sq.  ft.,  at  any  definite  depth,  and  D  =  internal  diam- 
eter in  inches.  T=  total  tension  on  12"  width. 

The  area  of  steel  to  take  care  of  this  tension  is  found  by  di- 
viding the  tension  by  the  safe  unit  stress  in  the  steel.  By  calcu- 
lating the  tension  for  each  foot  in  width  the  closest  economy 
may  be  obtained  in  design. 

The  least  thickness  of  concrete  should  be  four  inches  to  a 
depth  of  about  six  feet,  but  for  deeper  tanks  the  bottom  thickness 
in  inches  should  be  equal  to  h/2  in  feet,  and  the  thickness  at 
a  point  six  feet  from  the  top  can  be  four  inches,  remaining  at  that 
to  the  top,  while  the  remainder  of  the  wall  gradually  increases  to 
the  maximum  thickness  at  the  bottom. 

There  should  be  some  vertical  steel  to  help  preserve  the  in- 
tervals between  the  horizontal  rings,  and  if  the  tank  is  a  very 
high  one  this  vertical  steel  should  be  proportioned  to  resist 
stresses  caused  by  wind  against  the  tank  as  a  circular  hollow 
cantilever  beam.  This  will  now  be  discussed,  as  it  is  also  of 
value  in  designing  chimneys. 

For  chimneys  the  depth  of  the  foundation  is  from  1/10  to 
1/6  the  height.  If  the  ratio  of  base  to  height  is  small  the  foun- 
dation must  be  spread,  and  it  is  often  made  in  the  form  of  a 
truncated  cone  or  pyramid.  When  reinforced  concrete  is  not 
used  a  common  rule  is  to  make  the  width  of  the  foundation  equal 
to  the  width  of  the  chimney,  or  tank,  plus  one-tenth.  The  bot- 
tom of  the  foundation  is  one  and  one-half  times  that  width. 
When  a  reinforced  concrete  base  is  used  the  upward  reaction  on 
the  base  is  the  action  of  a  load  on  a  cantilever  beam  having  a 
length  equal  to  the  distance  from  the  edge  of  the  tank  or  chim- 
ney to  the  edge  of  the  foundation,  and  pressure  per  sq.  ft.  at  edge  is, 

F  = 


The  pressure  of  the  wind  will  be  50  Ibs.  per  sq.  ft.  on  a  plane 
equal  in  height  to  the  chimney,  or  tank,  and  having  a  width  equal 
to  the  outside  diameter.  Through  the  center  of  gravity  of  the 
structure  drop  a  vertical  line  and  make  it  equal  in  length  to  the 
weight.  Through  this  point  draw  the  total  amount  of  the  wind 
pressure  and  obtain  the  resultant.  If  it  falls  outside  the  middle 
third  of  the  base  then  it  requires  reinforcement.  Having  the  wind 
pressure  the  bending  moment  at  the  bottom  is  found  and  it  is  re- 
quired to  find  the  steel  to  resist  it. 


62  Reinforced  Concrete. 

To  find  the  resisting  moment  of  the  steel  we  have  to  find  the 
section  modulus  of  a  hollow  steel  cylinder  and  to  find  the  resist- 
ing moment  of  the  concrete  we  have  to  find  the  section  modulus 
of  a  hollow  concrete  cylinder.  The  thickness  of  the  concrete  in 
this  case,  for  a  high  structure,  will  be  found  by  taking  a  minimum 
thickness  at  the  top  and  maintaining  it  until  a  depth  is  reached 
where  the  load  is  about  200  Ibs.  per  sq.  in.  The  thickness  will  then 
be  increased  from  time  to  time  so  the  pressure,  due  to  the  weight 
of  the  concrete,  will  at  no  time  exceed  200  Ibs.  per  sq.  in.  This  will 
then  give  the  thickness  of  the  shell  at  the  bottom,  which  is  the 
thickness  we  will  use  in  the  calculations. 

/   d4— di'\ 
The  section  modulus  for  a  hollow  beam  is  S  =  0.09821 — ^ — 1 

in  which  d  =  external  diameter  in  inches,  and  di—  internal  diameter 
in  inches. 

When  M  =  bending  moment  in  inch  Ibs 
S  =  section  modulus  in  inches. 
f  =  fibre  stress  in  Ibs.  per  sq.  in. 

M  =  Sf ;  S  =  -JJT;  f  =  -g-. 

To  find  the  section  modulus  for  the  steel  reinforcement  con- 
sider it  as  a  thin  sheet  arranged  in  a  cylindrical  form,  and,  put- 
ting the  two  diameters,  d  and  di  in  inches,  find  S.  Divide  the 
overturning  moment  in  inch  Ibs.  by  the  fibre  stress  and  get  a 
second  value  of  S.  Take  the  area  in  sq.  ins.  of  the  steel  in  one 
circumferential  foot  of  the  structure  as  assumed  by  the  thin 
sheet,  and  multiply  by  the  second  value  of  S,  obtained  by  divid- 
ing the  moment  by  the  fibre  stress  in  the  steel.  Divide  the  quo- 
tient by  the  first  value  of  S,  found  by  the  foregoing  formula, 
and  the  result  will  be  the  number  of  inches  of  steel  (area  of 
vertical  rods)  required  in  each  foot. 

To  find  the  maximum  intensity  of  compression  in  the  con- 
crete is  the  next  step.  Having  already  obtained  diameters  for 
the  concrete,  find  S  by  the  formula.  To  get  the  second  value  of 
S  we  take  one-third  of  the  first  value  of  S  for  the  steel  and  mul- 
tiply it  by  n  (the  ratio  of  the  moduli  of  elasticity)  and  add  to  it 
this  first  value  of  S  of  concrete.  Dividing  the  bending  moment 
by  this  second  value  of  S  for  the  concrete  we  get  the  pressure 
per  sq.  in.  on  the  windward  side  of  the  structure.  To  this  must 
be  added  the  unit  weight  of  the  structure,  of  course,  and  we  thus 
get  the  total  compression  in  the  concrete  at  the  base  on  the 
windward  side.  If  it  exceeds  350  Ibs.  per  sq.  in.  the  thickness  at 
the  base  must  be  increased. 


Footings.  63 

The  steel  rods  are  vertical  and  must  extend  into  the  base  far 
enough  to  have  sufficient  bond. 

Footings. 

The  area  of  the  footing  under  a  wall  must  be  sufficient  to 
keep  the  load  within  the  permissible  amount.  In  the  case  of  a 
wall  the  footing  must  project  a  certain  number  of  feet  on  each 
side  so  that  it  will  really  be  like  two  cantilever  beams,  each 
carrying  half  the  load.  The  width  of  each  beam, will  be  12  inches 
and  the  length  will  be  the  quotient  found  by  dividing  half  the 
load  by  the  permissible  load  per  square  foot  on  the  foundation. 

The  shear  at  the  edge  of  the  wall  will  be  equal  to  the  load 
on  the  beam  at  that  side  and  we  may  assume  not  more  than  300 
Ibs.  per  sq.  in.  for  direct  shear.  This  will  fix  a  minimum 
thickness  for  the  slab.  The  calculation  for  bending  moment 
will,  give  a  thickness  and  the  greater  thickness  is  to  be  selected. 
The  thickness  given  by  the  bending  moment,  however,  will  be 
used  to  proportion  the  steel.  The  steel  rods  must  run  clear 
across  from  one  edge  to  the  other,  under  the  wall,  near  the  bot- 
tom of  the  footing  slab.  They  must  be  of  a  size  that  will  furnish 
sufficient  area  for  bond  and  then  the  amount  of  steel  for  stirrups 
should  be  calculated  to  take  care  of  internal  stresses.  These 
stirrups  will  be  close  together  just  under  the  edges  of  the  wall. 
(See  pages  25,  31  and  36.) 

Footings  under  columns  will  have  enough  square  feet  in 
them  to  spread  the  load  sufficiently  and  the  steel  will  be  propor- 
tioned on  the  theory  of  the  column  standing  on  two  beams 
crossing  under  the  column,  each  equal  in  length  to  the  width  of 
the  slab.  There  will  then  be  four  cantilever  beams,  each  having 
a  width  equal  to  the  thickness  of  the  column  and  a  length  equal 
to  their  projection  beyond  the  column.  To  help  bind  the  base 
together,  diagonal  rods,  equal  in  number  to  the  rods  in  each  of 
the  beams  mentioned,  will  run  to  the  corners.  Sometimes  rods 
are  placed  around  the  outside  as  well  to  connect  the  ends  of 
the  cross  rods.  Usually  steel  is  placed  both  ways  like  a  net- 
work, or  expanded  metal  or  wire  fabric  are  used  in  addition. 
Investigations  must  be  made  for  shear  and  bond,  and  stirrup 
reinforcement  provided  where  found  necessary. 

In  putting  down  footings  it  is  well  to  place  three  or  four 
inches  of  concrete  and  lay  the  steel  on  this;  in  the  footing  put 
steel  plates  on  which  to  rest  the  vertical  steel. 


CHAPTER  V. 
DESIGN  AND  COST. 

Do  not  approach  the  design  of  a  reinforced  concrete  structure 
with  the  idea  that  the  material  is  miraculously  endowed  with  won- 
derful properties  and  has  utterly  changed  its  character  because  of 
the  reinforcement 

A  noted  Frenchman,  M.  Considere,  made  some  experiments 
on  beams  by  loading  them  until  they  broke.  He  sawed  slices  from 
the  bottom  underneath  the  reinforcement,  and  claimed  to  have 
discovered  that  concrete  beams,  when  reinforced,  stretched  ten 
times  as  much  in  the  bottom  as  plain  beams,  without  injury  to  the 
concrete. 

So  far  as  an  ordinary  mortal  could  see,  the  concrete  had  the 
appearance  of  ordinary  concrete.  There  was  nothing  to  distinguish 
it  except  the  fact  that  the  professor  said  it  was  different.  Strange 
to  say,  when  separated  from  the  steel,  it  was  exactly  as  strong  in 
tension  and  compression  as  before. 

Professor  Turneaure,  of  the  University  of  Wisconsin,  was 
one  of  the  unbelievers  in  this  miracle,  so  made  tests  of  his  own. 
He  placed  beams  in  a  testing  machine  with  the  reinforced  side  on 
top.  Instead  of  resting  them  upon  supports  and  having  the  load 
applied  as  weight,  he  applied  pressure  at  the  bottom,  and  the  sup- 
ports were  on  top  at  the  ends.  As  the  pressure  was  applied,  the 
beams  bent  upward,  and  when  water  was  poured  on  the  surface 
fine  dark  lines  appeared.  When  the  beam  was  removed  from  the 
testing  machine  and  pieces  sawed  from  it  for  testing,  it  was  dis- 
covered that  when  cut  between  two  dark  lines  there  was  no  ap- 
parent change  in  the  general  properties  of  the  concrete.  When  a 
piece,  however,  included  one  of  the  fine  dark  lines  it  fell  apart,  thus 
proving  the  line  to  be  a  crack. 

This  set  of  experiments  showed  that  the  concrete,  when  rein- 
forced, was  the  same  old  concrete.  Instead  of  having  miraculous 
properties  developed  by  the  reinforcement,  it  was  the  reinforce- 
ment that  stretched.  The  concrete  simply  developed  innumerable 
fine  cracks.  If  the  adhesion  is  good,  these  cracks  are  uniformly 
distributed  and  are  not  visible'' to  the  eye.  In  fact,  some  may 
require  a  remarkably  good  microscope  to  discover  them. 

64 


Design  and  Cost.  65 

A  very  few  men  dispute  the  experiments  of  Professor  Tur- 
neaure  as  being  not  conclusive,  but  by  the  majority  of  engineers 
they  are  accepted  as  establishing  the  true  action  of  concrete  in  the 
tensile  side  of  a  reinforced  beam.  If  this  is  the  fact,  then  it  is 
proven  that  failure  begins  in  a  reinforced  concrete  beam  from  the 
moment  the  load  begins  to  act.  Cracks  form  just  as  soon  as  the 
load  exceeds  the  tensile  strength  of  the  concrete,  and  these  cracks 
continually  enlarge  until  the  beam  fails,  either  by  the  steel  parting 
or  by  the  concrete  crushing  at  the  top,  alone  or  in  combination 
with  breaks  caused  by  internal  stresses  in  the  concrete. 

Assuming  that  cracks  open  in  the  bottom  under  the  steel,  the 
importance  of  having  the  steel  protected  by  plenty  of  mortar  un- 
derneath is  seen.  A  very  small  crack  will  admit  moisture  and 
corrosion  commences.  This  is  a  warning  not  to  attempt  to  use 
too  small  a  percentage  of  reinforcement,  nor  too  small  a  factor 
of  safety.  Deflection  must  be  considered,  for  when  a  beam  deflects 
it  bends,  and  when  it  bends  the  concrete  underneath  the  steel 
cracks. 

Strictly  speaking,  there  is  no  modulus  of  elasticity  for  con- 
crete, for  the  reason  that  concrete  is  not  a  uniform  material.  It 
is  no  more  unir.rm  than  stone,  so  far  as  mere  strength  is  concerned, 
and  every  one  knows  that  stone  varies  in  strength  in  the  same 
specimen.  The  variations  in  concrete  come  from  differences  in 
proportioning  the  mixture  and  also  in  mixing  the  aggregates.  This 
being  the  case,  the  term  "factor  of  safety"  is  a  misnomer.  There 
is  no  factor  of  safety  with  concrete  as  there  is  with  steel. 

What  we  know  about  concrete,  that  renders  it  suitable  for  use 
in  building  when  combined  with  steel  is: 

That  owing  to  the  presence  and  even  distribution  of  the 
cement,  it  is  more  durable  than  the  best  of  stone  when  exposed 
to  the  atmosphere; 

That  when  carefully  made,  with  the  aggregates  proportioned 
and  manipulated  as  experience  has  shown  to  be  best,  we  know 
that  a  stress  of  500  pounds  per  square  inch  in  compression  may  be 
used  with  a  reasonable  certainty  that  the  ultimate  strength  of  that 
particular  concrete  may  be  five  or  six  times  the  stress  allowed. 
As  steel  is  a  carefully  made,  homogenous  material,  such  a  ratio 
can  be  assumed  as  exact  through  every  portion,  and  can  be  termed 
a  factor  of  safety.  With  concrete,  however,  the  factor  of  safety 
is  entirely  an  assumption  which  applies  to  the  concrete  as  a  whole. 
It  may  be  large  for  some  portions  and  be  small  for  other  portions 
of  the  mass. 


66  Reinforced  Concrete. 

That  the  strength  of  concrete  depends  upon  the  character  of 
the  aggregates.  Thus  cinder  concrete  is  stated  to  be  one-half  as 
strong  as  stone  concrete.  Sandstone  concrete  is  not  so  strong  as 
concrete  made  of  basalt  or  granite.  Limestone  concrete  is  very 
strong  and  satisfactory  under  certain  conditions,  and  not  so  reliable 
when  conditions  are  not  right. 

That  the  strength  of  concrete  increases  and  its  resistance  to 
atmospheric  influences  is  greater  the  older  it  is,  for  the  cement 
protects  the  other  aggregates. 

That  in  setting  concrete  shrinks,  and  consequently  it  grips 
fast  all  steel,  or  anything  else  of  an  impervious  nature  that  is 
enclosed  within  its  mass.  This  gripping  action  is  entirely  physical 
and  not  chemical.  It  is  termed  adhesion,  and  this  adhesion  is 
said  to  be  impaired  by  continuous  vibratory  shocks,  and  is  known 
to  be  impaired  by  continuous  submersion  in  water.  This  impair- 
ment may  never  proceed  to  the  point  of  destruction  of  the  adhesion, 
but  if  high  stresses  are  used  in  the  steel  it  is  well  to  have  the 
additional  safeguard  of  mechanical  bond,  obtained  by  the  use  of 
deformed  rods  and  bars. 

On  the  point  of  adhesion  it  is  well  to  remember  that  there  is  no 
special  affinity  between  steel  and  concrete,  any  more  than  there  is 
between  oil  and  water.  To  test  this,  place  concrete  on  a  smooth 
steel  surface  and  let  it  set.  When  dry,  kick  it  off,  which  can  be  done 
easily.  Set  a  steel  I  beam  on  edge  and  plaster  the  space  on  one 
side  with  concrete,  or,  better,  set  a  board  alongside  as  a  form  and 
pour  concrete  into  the  space.  When  perfectly  set,  hit  the  other 
side  of  the  I  beam  with  a  hammer  and  see  the  concrete  drop  away. 

Put  a  flat  steel  bar  on  edge  across  a  shallow  box,  the  one 
edge  resting  on  the  bottom,  the  other  level  with  the  top,  thus 
making  a  partition.  Fill  the  box  with  concrete  and  allow  the 
concrete  to  set.  When  dry,  remove  the  sides  of  the  box,  and,  after 
the  material  is  thoroughly  set,  see  how  slight  a  blow  will  cause 
the  concrete  to  separate  from  the  steel. 

The  shrinkage  proceeds  from  the  outside  toward  the  interior. 
The  special  fact  that  enables  us  to  use  concrete  and  steel  in 
combination  is  that  each  material  expands  and  contracts  in  almost 
identical  degree  under  the  influence  of  changes  in  temperature. 
If  it  were  not  so,  then  changes  in  temperature  would  cause  each  to 
move  in  a  different  degree,  and  the  adhesion  would  soon  be  de- 
stroyed. 

When  it  is  known  that  the  adhesion  is  entirely  a  gripping 
action,  the  value  of  small  rods  and  bars  for  reinforcement  is  proven. 


Gripping  Action  of  Concrete.  67 

In  fact,  when  discussing  adhesion,  the  values  given  should  be  given 
to  half-inch  bars.  Bars  of  less  diameter  will  have  proportionately 
greater  and  those  of  larger  diameter  proportionately  smaller  ad- 
hesive value.  This  difference  probably  varies  as  the  cube  root  of 
the  diameters,  although  there  is  no  absolute  basis  yet  for  stating 
the  difference  to  exist  in  such  degree. 

In  his  own  practice  the  writer  has  the  space  between  reinforcing 
bars,  or  rods,  never  less  than  twice  the  thickness  or  diameter. 
Underneath  the  steel  the  minimum  thickness  is  twice  the  thick- 
ness or  diameter  of  the  steel,  except  when  the  steel  is  in  the  form 
of  wire,  when  the  least  covering  is  half  an  inch.  In  slabs  liable 
to  be  exposed  to  the  action  of  fire,  the  minimum  thickness  is  one 
and  one-half  inches  and  for  beams  two  inches.  For  columns  two 
inches,  and  for  tank  walls  subjected  to  constant  immersion,  two 
inches. 

The  gripping  action  of  concrete  should  not  be  too  greatly 
checked,  and  for  this  reason  round  rods  are  favored  by  many 
designers.  It  requires  no  argument  to  show  that  the  wet  material 
is  more  apt  to  set  well  in  contact  with  a  round  bar  than  with  a 
square  bar.  Assuming  very  low  unit  stresses  in  both  steel  and 
concrete,  the  use  of  plain  round  bars  is  entirely  defensible  for  90 
per  cent  of  the  structures  erected  in  reinforced  concrete.  The  other 
10  per  cent  may  be  in  situations  such  that  the  designer  feels  a 
deformed  bar  to  be  necessary.  To  discuss  the  deformed  bars  in 
the  market  in  this  connection  would  place  the  writer  in  an  em- 
barrassing position.  He  has  used  practically  all,  and,  as  before 
stated,  to  get  a  certain  strength  requires  a  certain  percentage  of 
reinforcement,  regardless  of  shape.  The  deformation  acts  as 
anchorage,  except  with  the  Kahn  bar,  where  it  performs  a  double 
function,  being  anchorage  as  well  as  web  reinforcement. 

A  round  bar  permits  the  material  to  flow  around  and  grip  it 
better  than  will  a  square  bar,  yet  it  does  not  offer  the  same  surface 
for  adhesion.  A  square  bar  twisted  gives  the  adhesive  surface, 
while  it  makes  practically  a  round  bar  with  corrugations  through 
which  the  concrete  may  readily  flow.  For  this  reason  a  square  bar 
twisted  is  economical,  as  every  square  inch  of  cross  section  is 
available  for  reinforcing  purposes,  while  the  twisting  gives  the 
mechanical  bond.  Some  men  claim  the  edges  cause  cracks  to  start 
when  the  concrete  is  shrinking.  Others  make  this  charge  against 
all  bars  not  having  rounded  edges.  The  writer  believes  most  of 
this  talk  to  be  purely  theoretical,  and  that  any  bar  in  the  market 
is  good,  provided  enough  area  is  used  to  give  the  desired  strength. 


68  Reinforced  Concrete. 

When  designing  a  structure,  go  over  the  design  carefully  sev- 
eral times.  If  wind  strains  are  to  be  feared,  it  is  wise  to  use 
round  bars  and  have  the  ends  threaded,  so  that  all  connections 
will  be  made  by  screwed  couplings.  Connect  columns,  walls  and 
girders  by  bolsters  or  brackets,  reinforced  to  take  care  of  twist- 
ing strains  liable  to  be  caused  by  wind  or  earthquake.  See  that 
all  connections  at  corners  and  at  beams,  girders  and  walls  are 
carefully  computed  and  not  merely  guessed  at. 

It  is  such  a  common  practice  to  make  a  continuation  of  rein- 
forcement by  simply  lapping  ends  past  a  few  inches  that  a  warn- 
ing must  be  sounded,  although  the  matter  was  dealt  with  fully 
in  Chapter  I.  Lapped  connections  greatly  increase  the  stresses 
in  the  concrete  at  those  points.  Screwed  connections  are  good. 
In  columns  the  ends  of  the  steel  should  rest  on  plates,  as  already 
mentioned,  and  the  ends  of  the  bars  should  be  milled.  A  con- 
tinuation should  be  made  inside  a  sleeve,  and  if  high  winds  are 
feared,  the  ends  should  be  connected  by  screwing. 

Bars  and  rods  should  be  wired  together  at  all  crossing  points 
to  preserve  the  intervals.  Black  stove  wire  is  generally  used.  This 
is  known  as  No.  18,  and  should  be  black,  as  galvanized  wire  is  not 
so  good  for  adhesion  as  black  wire.  No.  16  wire  is  favored  by 
many  engineers  as  being  stronger  than  No.  18,  and  a  number  of  men 
require  the  use  of  No.  14,  which  is  excessive  and  is  more  con- 
suming of  time  to  place  and  twist.  For  all-round  use  No.  16  is 
best,  but  requires  the  use  of  pliers,  whereas  No.  18  can  be  twisted 
by  hand.  The  way  pliers  disappear  on  a  job  is  an  argument  in 
favor  of  the  lighter  wire. 

Never  use  painted  or  coated  wire  for  reinforcement.  Galvan- 
ized wire  or  steel  rods  should  not  be  used  except  when  provided 
with  mechanical  bond.  The  galvanized  fabrics  in  the  market,  of 
course,  have  the  mechanical  bond  created  by  the  fastening  of  the 
crossed  wires.  A  slight  rusting  is  not  harmful.  The  writer  made 
some  experiments  several  years  ago  by  enclosing  slightly  rusted 
steel  in  wet  concrete.  After  a  year  the  blocks  were  broken  and 
the  steel  was  found  without  rust.  The  surrounding  concrete  was 
found  to  be  slightly  discolored.  When  the  rust  is  in  the  form  of 
scales,  it  should  first  be  removed. 

Many  buildings  are  weakened  by  holes  cut  at  random  through 
slabs  and  walls.  Common  sense  should  be  a  guide  here.  It  is 
well  to  remember  that  when  a  slab  is  made  the  strength  is  as- 
sumed to  be  that  of  the  slab  with  the  reinforcement  complete  and 
tied  from  support  to  support.  If  the  steel  is  cut,  it  is  equivalent 


Attention  to  Details.  69 

to  destroying  one  support,  and  the  action  of  the  slab  on  each  side 
of  the  hole  is  a  cantilever  action,  but  as  the  reinforcement  is  in  the 
bottom,  the  steel  is  of  no  assistance.  This  is  an  argument  in  favor 
of  double  reinforcement,  in  addition  to  the  argument  that  may 
be  presented  from  the  fire  protection  standpoint. 

Holes,  therefore,  should  be  located  while  the  structure  is 
being  planned  and  the  reinforcement  arranged  accordingly.  The 
reinforcement  should  generally  be  in  the  form  of  two  double  rein- 
forced beams  each  way,  one  on  each  side  of  the  hole,  or  the  slab 
can  be  designed  as  a  cantilever  beam  on  the  four  sides  of  the  hole, 
the  remainder  of  the  slab  resting  on  and  being  carried  by  the  can- 
tilevers. 

As  the  fibre  stresses  in  wood  and  in  reinforced  concrete  differ 
slightly,  the  sizes  of  beams  and  thickness  of  floors  in  a  slow- 
burning  wood  construction  building  and  a  reinforced  concrete 
building  are  near  a  size.  The  reinforced  concrete,  however,  will 
be  more  massive  than  the  wood. 

For  this  reason  some  men  become  panic-stricken  when  they 
see  the  building  going  up,  and  are  apt  to  make  some  members 
smaller  or  lean  toward  the  danger  point  in  designing  because  "the 
thing  looks  too  big."  A  reinforced  concrete  structure  is  unlovely 
from  a  structural  standpoint.  In  the  preceding  chapter  an  example 
was  given  of  how  column  sizes  compared  in  different  materials. 
A  comparison  in  beams  would  be  even  more  striking. 

The  eye  accustomed  to  wooden  beams  as  the  biggest  beams 
required  to  give  certain  strength  does  not  like  the  appearance  of 
reinforced  concrete  beams,  and,  as  many  of  them  show  the  grain 
of  the  wooden  forms  and  the  gray  color  is  much  like  that  of 
seasoned,  weather-stained  wood,  a  reinforced  concrete  building 
sometimes  looks  like  a  big,  clumsy  wooden  structure.  Perhaps  a 
style  of  architecture  peculiar  to  reinforced ,  concrete  may  arise 
and  have  a  beauty  of  its  own  so  it  will  not  offend. 

Most  of  the  data  obtainable  about  cost  of  reinforced  con- 
crete work  is  misleading.  It  has  generally  been  given  out  by 
men  who  simply  were  on  the  work  at  intervals  in  the  capacity 
of  supervising  engineers  and  who  did  not  know  anything  of  the 
thousand  and  one  exasperating  delays  incident  to  the  work  and 
who  knew  nothing  of  the  dense  stupidity  of  the  laborers  often 
employed.  Sometimes  the  data  has  been  given  on  the  authority 
of  some  company  controlling  a  splendid  organization  and  all  of 
the  employes  were  skilled  men  working  to  standards  and  on 
only  one  class  of  work. 


70  Reinforced  Concrete. 

Look  where  one  will  it  is  almost  impossible  to  secure  actual 
cost  data  of  reinforced  concrete  work.  Most  of  the  work  is  done 
by  men  who  look  aghast  at  the  figures  when  a  job  is  completed 
and  are  ashamed  to  publish  the  costs.  They  seem  so  much 
higher  than  current  published  data  that  they  think  it  a  reflec- 
tion upon  themselves  and  wish  to  try  another  job  before  giving 
out  figures. 

Their  wjork  is  comparatively  small  and  no  jobs  last  long 
enough  to  enable  them  to  perfect  an  organization.  Neither  do 
jobs  follow  quickly  enough  to  enable  them  to  retain  men  who 
have  been  broken  in  as  foremen.  This  class  of  work,  not  done 
by  regularly  organized  companies  engaged  in  training  skilled 
foremen,  carpenters  and  laborers  on  one  job  for  employment  on 
another,  is  the  real  criterion  for  gauging  the  cost  of  work. 

Much  is  written  about  the  low  cost  of  reinforced  concrete 
work  because  of  the  fact  that  unskilled  labor  is  largely  employed. 
A  visit  to  .a  good  job  will  show  that  the  unskilled  laborers  are 
in  the  minority.  For  every  laborer  who  pushes  a  wheelbarrow 
and  shovels  concrete  materials  there  will  be  employed  a  carpen- 
ter or  skilled  man. 

While  unskilled  labor  can  be,  and  is  largely,  employed, 
there  is  a  vast  difference  between  the  unskilled  man  who  is  born 
and  reared  in  America,  who  can  understand  English,  and  the 
unskilled  foreigner  who  has  to  be  addressed  in  the  sign  lan- 
guage. Unskilled  laborers  are  divided  into  two  classes,  the 
intelligent  and  the  unintelligent.  The  intelligent  ones  are  the 
kind  to  employ  in  reinforced  concrete  work,  for  the  various 
operations  are  rapidly  assuming  the  importance  of  trades.  After 
a  few  months'  work  the  active  intelligent  laborer  has  a  right  to 
be  classed  among  skilled  workers.  Intelligent  unskilled  laborers 
are  divided  into  rapid  and  slow,  drunkards  and  nondrinking 
men,  men  who  care  and  men  who  take  no  interest  in  anything 
except  the  whistle  and  the  pay  check.  The  success  of  the  con- 
tractor can  be  gauged  by  his  luck  in  picking  up  good  men. 

Carpenters  have  been  mentioned.  The  men  who  apply  for 
jobs  as  carpenters  on  this  class  of  work  are  divided  into  wood 
butchers,  bluffers,  saw  and  hammer  men,  half  trained  appren- 
tices, sidewalk  and  fence  builders,  cabinet  makers,  inside  fin- 
ishers, millwrights,  bridge  and  trestle  builders  and  good  plain 
ordinary  old-fashioned  carpenters.  The  best  carpenters  are  men 
who  have  really  learned  their  trade  and  who  have  worked  some 
years  in  small  towns.  Such  men  generally  take  to  the  work  as 


Kind  of  Men.  71 

ducks  to  water.  All  the  others  above  enumerated  have  to  be 
taught.  Some  never  learn.  Form  and  scaffold  work  for  rein- 
forced concrete  jobs  call  for  a  distinct  class  of  woodworkers 
and  if  they  can  be  obtained,  time  and  money  are  saved. 

The  average  job  of  reinforced  concrete  is  done  by  men 
who  commence  the  work  without  a  skilled  worker  to  assist. 
They  must  advertise  for  men  and  try  to  select  from  the  appli- 
cants such  men  as  they  think  may  develop.  At  first  they  take 
all  who  come  and  begin  to  weed  and  select  after  a  start  has 
been  made.  For  weeks  they  conduct  a  kindergarten  and  just 
as  a  good  working  force  is  developed  may  be  discharged  and  a 
hustler  comes  who  takes  the  trained  crew  and  makes  excellent 
progress. 

It  must  be  remembered  that  skilled  men  in  concrete  work 
are  hard  to  find,  although  the  streets  are  full  of  men  making 
great  claims  of  proficiency.  The  really  skilled  men  are  in  the 
permanent  employ  of  the  men  who  trained  them  or  are  in 
well-organized  unions  and  averse  to  leaving  the  larger  cities. 
It  is  well  to  be  very  careful  in  taking  men  who  claim  to  have 
had  experience.  So  many  contractors  (and  engineers  and  ar- 
chitects as  well)  are  criminally  careless  in  placing  reinforcement 
and  looking  carefully  after  details  that  a  large  number  of  ex- 
perienced men  are  abroad  who  can  not  be  trusted  to  do  any- 
thing well  on  such  a  job  except  to  "hustle  'er  tru'." 

An  ordinary  reinforced  concrete  job  has  carpenters  and 
their  helpers,  making,  setting  and  removing  forms;  men  plac- 
ing, altering  and  removing  scaffolds  and  changing  running 
plank;  a  steel  yard  where  steel  is  assorted  according  to  sizes 
and  lengths  and  men  engaged  in  bending  and  cutting  steel; 
men  placing  steel  in  position  before  the  forms  are  placed ; 
men  cleaning  concrete  and  steel  ahead  of  'the  forms  and  men 
putting  in  concrete.  The  unskilled,  low  browed  unintelligent 
laborer  has  really  no  place  except  between  the  handles  of  a 
wheelbarrow  and  it  takes  many  of  a  superior  kind  to  keep  the 
work  so  fixed  that  a  few  of  the  stupid  ones  can  be  kept  moving. 
What  is  wanted  on  such  work  are  handy  men  possessing  con- 
siderable intelligence  who  will  do  anything,  even  to  pushing  a 
wheelbarrow  if  laborers  run  short. 

There  is  nothing  in  low  cost  labor.  Really  cheap  labor  is 
well  paid  intelligent  labor.  When  a  man  is  efficient  he  must  be 
paid  correspondingly  well  for  there  is  a  constant  demand  for 
s,uch  men.  The  man  at  the  head  can  not  be  always  running  a 


72  Reinforced  Concrete. 

school.  It  is  argued  that  there  is  nothing  great  in  placing  steel 
or  placing  concrete.  Neither  is  there  anything  great  in  making 
a  table,  but  the  table  made  by  the  amateur  does  not  look  like 
the  table  of  the  craftsman.  Reinforced  concrete  work  requires 
intelligent  men,  but  generally  several  hundred  men  go  through 
a  job  before  fifteen  good  ones  are  secured  and  twice  that  number 
before  one  decent  foreman  can  be  obtained. 

All  concrete  work  is  not  alike,  hence  the  unreliability  of 
most  of  the  published  cost  data  as  a  basis  for  estimates.  Some 
structures  are  made  completely  of  concrete  with  thin  walls. 
Some  have  thick  walls.  In  some  the  reinforcement  is  vertical 
and  in  some  it  is  horizontal.  In  some  all  material  is  wheeled 
in  barrows  to  the  mixer  and  in  barrows  from  the  mixer  to  the 
forms.  In  some  places  automatic  elevators,  super-hoppers  and 
grab  buckets  and  a  multitude  of  labor-saving  devices  are  em- 
ployed. 

Some  buildings  have  merely  columns  and  girders  and  beams 
of  reinforced  concrete  with  reinforced  concrete  floors  and  roofs 
and  the  exterior  walls  of  brick  with  interior  walls  of  tile. 
There  are  good  systems  in  use  for  flooring,  involving  a  com- 
bination of  reinforced  concrete  beams  and  tile.  Some  systems 
use  frames  of  I  beams  instead  of  concrete  beams.  Some  build- 
ings have  been  erected  having  all  the  structural  framework  of 
reinforced  concrete  cast  in  shops  near  the  work  and  erected 
like  steel  after  the  concrete  has  hardened  thoroughly. 

Remember  that  in  erecting  a  reinforced  concrete  structure 
with  solid  walls  two  complete  wooden  structures  are  erected 
and  taken  down.  Nearly  all  the  lumber  is  afterward  useless 
unless  the  forms  are  made  in  interchangeable  panels  and  a  new 
job  is  at  hand  so  they  can  be  used  immediately.  Scaffolds  for 
ordinary  buildings  do  not  require  to  be  so  strong  as  scaffolds 
for  concrete  work,  so  the  costs  for  scaffolding  and  running 
plank  are  high. 

The  greatest  improvement  in  the  future  must  be  in  the  line 
of  reduced  cost  for  forms  and  simplicity  of  forming.  Many  build- 
ers are  ashamed  to  tell  what  their  forms  cost.  Each  time 
they  bid  higher  on  work  they  blame  the  increased  prices  to 
the  increased  labor  and  material  prices. 

The  cost  of  concrete  can  readily  be  figured.  The  cost  of 
getting  materials  to  the  mixer  and  of  mixing  them  can  easily  be 
figured.  The  cost  of  getting  concrete  from  the  mixer  to  the 
walls  depends  upon  the  length  of  run  and  convenience  of 


Cost  of  the  Work.  73 

arrangement  of  the  running  plank.  In  a  well  arranged,  well 
managed  job,  $1.00  per  yard  should  take  the  stone,  sand  and 
cement  from  the  stock  pile  and  shed  through  the  mixer  and  into 
the  wall. 

The  forms  can  not  be  figured  on  a  yardage  basis,  except  in 
the  case  of  a  company  engaged  in  certain  kinds  of  work  of  a 
standard  nature.  After  several  jobs  a  per  yard  cost  for  scaf- 
fold and  forms  can  be  obtained.  It  will,  however,  not  be  a  safe 
guide  for  other  work.  To  estimate  the  form  work,  the  style 
of  forms  to  be  used  must  first  be  decided  upon.  Then  figure  il 
on  a  per  thousand  foot  basis.  With  cheap  carpenters  it  will 
cost  from  $8.00  to  $20.00  per  thousand  to  make  forms.  With 
good,  higher  paid  carpenters  it  will  cost  from  $5.00  to  $7.00 
per  thousand  to  make  forms.  It  will  cost  about  $6.00  per  thou- 
sand to  place  them  and  about  the  same  to  take  them  down  and 
clean  them  for  use  again. 

There  is  a  big  waste  of  lumber  in  form  work  and  to  reduce 
this  waste  only  carpenters  or  the  best  of  the  workmen  should 
take  down  old  forms.  If  the  wheelbarrow  man  is  put  at  the 
work  he  will  ruin  them.  The  cost  of  cleaning  up  and  the  general 
expense  on  a  job  will  be  nearly  $2.00  per  cubic  yard  of  concrete. 
To  estimate  work  exactly,  careful  detailed  drawings  should  be  made 
of  the  forms.  They  should  be  designed  as  carefully  as  the  rest  of 
the  building. 

As  some  approximate  rules  are  always  wanted,  the  writer  can 
offer  the  following  as  fitting  very  closely  actual  conditions  on  a 
job  having  experienced,  well-trained  foremen,  and  among  the  labor- 
ers a  good  proportion  of  men  who  have  worked  on  similar  jobs. 
This  rule  applies  to  ordinary  building  construction,  for  the  cost 
per  yard  for  sewers,  culverts,  retaining  walls,  etc.,  is  much  less 
than  for  buildings. 

Get  exact  costs  of  sand,  stone  and  cement  delivered  on  the  job 
and  reduce  the  costs  to  cubic  yards  of  concrete.  To  this  add  $5.00 
per  cu.  yd.  for  steel.  This  will  be  one-half  =  3/6,  the  cost  of  the 
concrete  per  cubic  yard  in  place.  The  labor  on  concrete  and  steel 
will  be  1/6  and  the  material  and  labor  on  forms  will  be  2/6.  For 
average  buildings  containing  about  2,000  cu.  yds.  of  concrete  this 
will  be  about  true.  Add  2  per  cent  to  cost  for  each  100  cu.  yds. 
less  than  2,000.  Complicated  work  will  increase  the  cost  greatly. 
To  this  must  be  added  cost,  or  rent,  of  plant,  and  the  profit  of  the 
contractor. 


74  Reinforced  Concrete. 

If  the  materials  are  obtained  at  exceptionally  low  prices,  of 
course  the  above  rule  does  not  hold.  It  holds  for  average  pay  in 
the  locality  in  which  the  work  is  done,  for,  left  without  a  union 
organizer  to  run  up  pay,  laborers  in  different  sections  are  generally 
paid  what  they  earn.  It  is  always  best  to  pay  ruling  rates  of  wages 
everywhere  and  not  raise  the  pay,  except  to  good  men. 

Sometimes  men  are  frightened  when  estimating  on  reinforced 
concrete  work  because  the  costs  run  so  high.  While  the  cost  of 
the  building  seems  to  be  all  right,  the  cost  per  yard  of  concrete 
seems  fearfully  high.  A  common  sense  rule  is  to  consider  that  a 
reinforced  concrete  building  does  not  cost  less  than  a  brick  build- 
ing equally  as  well  constructed.  The  cost  of  a  brick  building  be- 
ing, say,  15  cents  per  cubic  foot  measured  from  the  basement  floor 
to  the  average  height  of  the  roof,  with  the  length  and  breadth 
taken  as  over  all  dimensions,  make  first  an  estimate  of  the  rein- 
forced concrete  building  in  that  way.  Then  go  through  the  plans 
carefully,  taking  out  the  exact  yardage.  Dividing  the  total  esti- 
mated cubic  foot  cost  by  the  yards  will  give  a  cost  per  yard  close 
enough  for  a  check  on  the  careful  detailed  computations  that  will 
later  be  made  by  the  careful  estimator. 

The  writer  would  like  to  see  more  men  making  money  at  this 
class  of  work  and  knows  of  many  who  have  lost  money  through 
wrong  estimates,  or  through  rushing  into  work  with  ideas  fixed. 
Left  to  himself,  the  experienced  man  will  generally  get  out  a  good 
plan  and  a  close  estimate  of  cost.  There  is  so  much  irresponsible 
matter  floating  around  in  papers  about  reinforced  concrete  that 
few  designers  are  given  a  free  hand  in  the  design  and  none  of  them 
are  allowed  to  make  a  correct  estimate.  The  employer  will  always 
declare  the  estimate  "Too  high  I"  and  give  instances  of  work  he  cas- 
ually read  about,  or  some  forgotten  individual  told  him  about. 
As  a  result  few  buildings  in  this  material  are  erected  at  the  esti- 
mated cost.  When  the  owner  has  his  work  done  on  a  percentage 
basis  it  falls  on  him,  but  if  some  contractor  new  at  the  business 
takes  the  contract  on  poor  information  he  is  ruined. 

Good  work  costs  money,  and  work  of  a  certain  grade  differs 
little  in  cost,  no  matter  what  the  material.  If  reinforced  concrete 
is  absolutely  fireproof,  earthquake-proof,  everlasting  and  never 
needs'  repairs,  it  is  reasonable  to  suppose  that  for  such  perfection  a 
price  must  be  paid. 


CHAPTER   VI. 
FORMS. 

The  ideally  conducted  job  is  where  the  men  in  charge  of  the 
steel  hanging  o-et  out  of  the  way  of  the  form  placers  so  the  forms 
may  be  filled.  The  steel  should  be  placed,  forms  erected,  concrete 
poured,  additional  steel  placed,  forms  re-erected  and  concrete 
poured  again,  all  without  a  hitch  and  without  the  mixer  having  to 
stop.  As  a  matter  of  fact  it  is  almost  an  impossibility  to  get  the 
average  sized  job  so  well  organized.  On  very  large  jobs  and  on 
concrete  work  where  there  is  no  reinforcement  and  where  the  walls 
are  comparatively  thick  it  must  be  done  and  is  done  right  along. 

The  chief  reason  for  delay  is  in  the  setting  or  erection  of  forms 
and  the  intelligence  and  experience  of  the  men  charged  with  the 
work  of  form  erection  and  changing.  On  comparatively  thick  walls 
the  time  it  takes  to  do  the  form  work  is  seldom  sharply  drawn  to 
one's  attention  for  it  takes  so  long  to  fill  such  walls  that  the  form 
workers  keep  ahead  of  the  concrete  gang  without  trouble.  It 
takes  as  long,  however,  to  erect  forms  for  a  thin  wall  as  for  a 
heavy  wall  and  sometimes  considerably  longer,  for  thin  walls  are 
generally  cut  up  with  pilasters  or  panels.  The  pouring  of  the 
concrete,  however,  is  almost  as  rapidly  done  in  a  thin  wall  as  in  a 
thick  one  and  as  there  is  so  much  less  concrete  to  pour  the  con- 
crete gang  soon  overtakes  the  form  gang. 

Because  of  this  the  cost  of  forms  per  cubic  yard  of  thin  walls 
is  much  higher  than  for  thick  walls.  It  requires  more  lumber  and 
while  it  takes  little  more  labor  the  labor  cost  is  higher  in  propor- 
tion, the  thinner  the  wall.  When  very  thin  walls  are  used  the  cost 
is  very  high  until  the  men  become  experienced  and  work  like 
machinery.  A  great  many  inexperienced  men  think  the  cost  of 
lumber  the  largest  item  but  when  lumber  costs  less  than  twenty-five 
dollars  per  thousand  and  inexperienced  men  alone  can  be  had  it 
will  be  found  least  expensive  to  sheet  right  along  up  and  pay  little 
attention  to  trying  to  use  the  material  several  times.  The  proper 
way  to  estimate  forms  is  by  square  foot  of  surface  and  not  per 
cubic  yard  of  concrete. 

Dressed  and  matched  lumber  is  good  for  use  once  or  twice 


76 


Reinforced  Concrete. 


LJ 

Secr.on  Tnfi 
FIG.   10 — FORM  PLANS   (GENERAL  FIREPROOFING  COMPANY). 


Men  and  Materials.  77 

and  is  not  such  a  good  material  for  re-use  as  plain  edged  lum- 
ber. Therefore  it  is  better  for  thick  walls  than  for  thin  ones, 
as  the  cost  per  yard  for  forms,  when  figured  that  way,  is  not 
high.  While  the  pressure  is  as  great  in  thin  as  in  thick  walls, 
considering  concrete  as  a  semi-fluid,  thinner  lumber  can  be 
used  to  advantage  in  thin  walls,  for  it  is  easily  handled  and  can 
be  tied  through  the  wall  readily  when  necessary. 

When  experienced  men  can  be  had  and  lumber  goes  over  the 
twenty-five  dollar  mark  per  thousand  then  it  will  pay  to  use  some 
form  of  panelling  or  try  the  "board  by  board"  method.  Whether 
panels,  or  single  boards,  or  the  studding  and  sheathing  method  is 
considered  best,  it  pays  to  use  the  boards  and  pieces  in  as  near 
standard  lengths  as  possible  for  they  might  be  worth  something 
after  using.  If  this  item  is  not  looked  after,  all  the  lumber  will  be 
fit  only  for  the  scrap  heap. 

The  writer  believes  the  best  carpenters  to  use  are  experienced 
men  who  have  thoroughly  learned  their  trade  and  the  boss  carpenter 
should  be  an  elderly  man  accustomed  to  handling  men.  A  few  first- 
class  men  can  do  much  more  work  than  cheaper  laborers.  It  is 
customary  to  hear  men  say  that  common  laborers  are  good  enough 
for  carpenters  on  a  concrete  job.  The  writer  begs  to  differ  with 
them  and  say  that  if  for  nothing  else  than  the  habit  a  trained 
man  has  of  staying  with  a  job,  the  experienced,  well-trained  car- 
penter is  best.  The  ordinary  unskilled  laborer  is  nomadic  and  as 
soon  as  he  thinks  he  has  learned  something  new  he  leaves  the  job 
to  sell  his  services  elsewhere.  The  writer  prefers  good  carpenters  as 
gang  bosses  and  under  each  good  carpenter  put  three  to  five  handy 
unskilled  laborers  as  apprentices  and  to  do  the  roughing  work. 
This  is  especially  true  if  any  calculation  is  made  on  using  the 
material  more  than  once. 

The  unskilled  or  incompetent  man  will  nse  many  more  nails 
than  the  trained  man.  This  means  expense  for  nails,  more  time 
putting  up  the  forms,  more  time  taking  them  down  and  the  likeli- 
hood of  ruining  a  great  deal  of  the  lumber  in  trying  to  take  it 
down  and  re-use  it. 

Fig.  11  represents  the  regulation  form  built  up  of  boards  nailed 
to  upright  studding  and  braced.  The  planks  may  be  of  any  thick- 
ness according  to  the  fancy  of  the  carpenter  or  of  the  contractor. 
The  studs  may  be  of  any  convenient  size  and  the  braces  and  posts 
against  which  they  rest  will  be  arranged  according  to  the  ideas  of 
the  men  in  charge.  For  this  style  of  forming  each  man's  fancy 
is  every  man's  guide.  Common  custom,  however,  seems  to  be 


78 


Reinforced  Concrete. 


coming  around  to  one  inch  boards  against  two  by  four  studs  set 
two  feet  apart.  The  braces,  however,  may  vary  in  size  from  two 
by  four  inches  to  six  by  six  inches  with  little  attention  paid  to  the 
manner  of  securing  the  ends. 


FIG.  11 — SIMPLE  BRACED  FORM. 

In  the  illustration  the  braces  are  bevelled  where  they  rest 
against  the  studs  and  are  supposed  to  be  fastened  by  "toenailing." 
This  is  very  poor  as  the  full  strength  of  the  brace  cannot  be  secured. 
In  spite  of  everything  the  nails  will  move  a  little  and  sometimes 
the  end  of  the  brace  will  slide  up  the  stud  and  pull  the  nails  entirely 
out 

The  upper  end  of  the  braces  should  be  cut  square  and  butt 
against  a  block  nailed  to  the  stud.  Instead  of  the  push  helping  to 
draw  the  nail  it  will  be  at  right  angles  and  the  nail  cannot  give 
without  shearing.  The  length  of  the  block  and  the  number  of  nails 
to  use  depends  upon  the  push.  These  things  are  seldom  figured 
out. 

The  trust  the  ordinary  wood  butcher  places  in  nails  is  pathetic, 
especially  after  a  bad  spill  caused  by  a  form  giving  way.  Plenty  of 
nails  will  not  always  do  the  work  which  should  be  done  by  plenty 
of  brain.  In  a  most  excellent  booklet  distributed  by  a  well  known 
cement  company  is  an  illustration  of  forms  braced  by  having  the 
braces  nailed  to  the  sides  of  the  studs  instead  of  butting  against 
them.  Instead  of  the  lower  end  of  the  braces  resting  against  posts 
or  on  sills  they  rest  simoly  upon  the  ground.  The  writer  has 
seen  many  braces  thus  placed  and  he  has  ceased  to  wonder  at  it 
being  done  but  does  wonder  at  the  mental  processes  wherefrom 


Bracing.  79 

such  ridiculous  results  proceed.     Common  sense  seems  to  be  at  a 
discount. 

It  is  common  to  hear  of  braces  giving  way  and  yet  in  every 
case  investigated  by  the  author  he  has  found  it  to  be  due  to 
improper  securing  of  the  braces,  except  when  a  rain  may  have 
softened  the  ground  into  which  the  supports  were  driven.  If  the 
ground  is  exceedingly  firm  it  is  sometimes  sufficient  to  drive  a 
post  as  shown  in  Fig.  11.  Whether  or  not  the  ground  is  firm  the 
best  and  safest  way  to  secure  the  lower  ends  of  braces  is  shown  in 
Fig.  12.  Here  a  line  of  posts  is  driven  and  a  two  by  six  or  heavier 
plank  laid  against  them.  Back  of  this  line  is  driven  a  second  line 
of  posts  with  a  brace  from  the  top  of  the  first  line  resting  against 
their  feet.  The  braces  from  the  forms  rest  against  the  plank  and 
it  is  wise  to  have  two 'hard  wood  wedges  at  the  end  to  take  up 
whatever  slight  movement  may  develop. 


FIG.  12 — METHOD  OF  SECURING  FORMS. 

While  on  this  subject  the  writer  wishes  to  say  he  does  not 
consider  bracing  to  be  good  practice  when  forms  are  used  on  both 
sides  of  walls  and  can  be  connected  by  wires  or  bolts  readily. 
Bracing  is  only  excusable  when  all  the  securing  can  only  be  done 
properly  from  the  outside  and  from  one  side.  Braced  forms  give 
way  more  readily  than  bolted  forms,  take  more  time  to  put  up,  use 
up  more  lumber  and  all  round  are  least  satisfactory  of  all  methods 
used.  Bolts  are  best  and  wires  next  with  braces  in  the  third  place 
as  regards  merit. 

When  braced  forms  give  way  it  is  generally  through  ignorance 
of  proper  methods  of  securing  the  braces.  The  times,  however, 
when  the  foundations  give  way  are  so  numerous  that  one  cannot 
be  absolutely  certain  a  properly  braced  form  will  not  burst.  When 


80 


Reinforced  Concrete. 


bolted  or  wired  forms  give  way  it  is  only  when  the  bolts  or  wire 
are    ignorantly   placed. 

Wire  is  very  expensive  for  it  requires  a  great  deal  of  material 
and  a  tremendous  amount  of  time.  When  the  forms  are  taken 
down  the  wire  projects  and  the  ends  must  be  cut  off.  They  leave 
rust  spots,  disfiguring  to  the  wall.  A  green  man  will  run  wire 
through  both  forms  and  twist  the  ends  to  form  a  loop.  On  one 
side  he  will  put  a  soft  wood  wedge  under  the  wire  thinking  that 
when  the  form  gives  he  can  drive  it  downi  and  tighten  the  wires. 
Vain  hope.  If  he  can  drive  the  wedge  at  all,  which  is  something 


Chair?   of /oops  for  thick 

FIG.   13 — METHOD  OF  WIRING  FORMS. 

to  consider,  he  will  either  shear  it  off  so  it  does  not  tighten  the 
wire,  or  he  will  only  succeed  in  driving  it  so  the  twisting  will  come 
undone  and  his  wedge  makes  things  worse.  To  use  wire  properly 


Tieing  the  Forms.  81 

it  should  be  passed  through  both  forms  and  twisted  inside  the  forms 
by  means  of  a  bolt  or  stick  used  as  shown  in  Fig.  13.  To  keep  the 
forms  the  right  distance  apart  a  piece  of  wood  should  be  placed 
beside  the  wire  and  left  there  until  the  concrete  reaches  that 
height,  when  it  is  fished  out.  It  happens  many  times  that  the  fishing 
is  forgotten  and  the  ends  of  the  stick  may  be  seen  when  the  form 
is  removed.  Or  it  may  happen  that  in  fishing  for  it  the  stick  is 
knocked  down  into  the  concrete,  there  to  remain,  a  weak  spot 
although  concealed  from  view.  This  happens  so  often  that  some 
men  use  pieces  of  concrete  instead  of  wood  for  spacers  and  make 
no  attempt  to  remove  them. 

Bolts  passing  through  the  wall  have  none  of  the  objections 
inherent  with  wire.  A  well  greased  bolt  can  be  removed  easily 
from  the  wall  after  the  concrete  has  set.  Trouble  always  ensues 
when  the  greasing  is  not  properly  performed.  Sometimes,  however, 
the  bolts  pass  through  paper  tubes  or  are  wrapped  in  several 
thicknesses  of  greased  paper  in  addition  to  being  greased.  Some 
men  use  hollow  tubes  of  concrete  through  which  pass  the  bolts, 
the  tubes  serving  also  as  spacers.  Wooden  spacers  used  with  bolts 
can  be  removed  as  soon  as  the  bolts  are  screwed  up.  With  wire 
the  tendency,  because  of  the  twisting,  is  to  draw  up  and  for  this 
reason  it  is  best  to  leave  the  spacer  in  place  until  the  pressure  of 
the  concrete  relieves  it.  Wire  will  give  a>  little  and  this  give 
cannot  be  taken  up.  A  bolt,  however,  is  secured  by  a  nut  on  the 
end  bearing  against  a  washer.  When  the  nut  has  been  screwed 
down  far  enough  the  spacer  can  be  removed.  If  the  form  does  get 
a  little  slack  it  will  move  out  under  the  pressure  of  the  concrete 
until  a  bearing  is  obtained  against  the  washer.  If  the  forms  give 
while  the  concrete  is  being  poured  the  nuts  can  be  tightened. 

While  wires  leave  rust  spots,  bolts  leave  holes.  These  holes 
are  generally  filled  with  a  neat  cement  paste  pushed  in  with  a  small 
stick.  If  the  wall  is  to  be  watertight  the  paste  has  mixed  with  it 
some  waterproofing  material.  The  grease  with  which  the  bolts 
were  treated,  or  the  paper  tube  left  in  the  wall  will  not  allow  a 
perfect  seal  so  it  is  almost  impossible  to  secure  a  water  tight  wall 
when  bolts  alone  are  used. 

While  holes  on  the  surface  may  be  filled  and  thus  sightliness 
be  preserved,  the  hole  through  the  body  of  the  wall  is  an  objection. 
Several  arrangements  have  been  made  to  overcome  this  by  using 
short  bolts  connected  to  wire  loops  in  the  body  of  the  wall.  The 
bolts  being  greased  are  withdrawn  when  the  forms  are  removed, 
leaving  the  wire  loops  and  thus  sealing  the  wall.  While  many  such 


82 


Reinforced  Concrete. 


devices  are  in  use  the  writer  for  years  has  used  ordinary  thumb 
nuts  connected  by  wire  loops  as  shown  in  Fig.  13.  A  machine  for 
making  the  loops  is  illustrated  in  the  chapter  following.  When 
one  loop  is  not  long  enough  several  may  be  connected  in  chain 
form  as  shown.  The  small  surface  holes  left  by  the  bolts  may  be 
plugged  with  neat  waterproofed  cement,  although  the  greasing  is 
an  objection,  for  it  interferes  with  the  bond. 

Unless  the  faces  of  the  forms  are  smooth  and  clean  the  surfaces 
will  be  bad.  How  to  overcome  roughness  of  surface  on  concrete, 
due  to  forms,  will  be  taken  up  in  the  next  chapter.  Tables  to 
determine  proper  sizes  and  spacing  for  braces,  wires  and  bolts  will 
also  be  given  there. 

The  form  illustrated  in  Fig.  11  is  usually  made  by  erecting 
studding  and  nailing  the  boards  to  the  inside  when  the  walls  are 


FIG.  14 — FORMS  OF  MATCHED  LUMBER. 


Dressed  and  Matched  Lumber.  83 

thick.  If  the  walls  are  thin  the  boards  are  nailed  to  the  studding 
while  lying  down  and  then  the  whole  side  is  raised,  precisely  like 
sheathing  the  side  of  a  wooden  house  when  erected  close  to 
another  house.  A  departure  is  made  by  erecting  the  studding  and 
putting  in  one  board  at  a  time.  The  lower  board  is  set  against 
the  studding  and  filled  with  concrete  when  a  board  is  placed  on 
top  and  the  work  continues  in  this  manner  until  a  height  of  eight 
or  ten  feet  is  reached.  No  nailing  is  required  except  for  an  occa- 
sional four  or  sixpenny  nail  to  merely  keep  the  boards  from  fall- 
ing down. 

By  starting  with  one  board  at  a  time  a  foot  of  concrete  per 
day  can  be  assured  on  a  very  large  building  and  it  should  be  pos- 
sible to  keep  the  mixer  going  all  the  time.  When  a  height  of  about 
eight  feet  is  reached  a  plate  is  placed  on  the  top  of  the  studs  and 
another  set  started.  At  the  bottom  they  are  wired  through  the 
wall  and  when  the  concrete  has  gone  up  a  foot  or  two  on  the 
second  set  the  lower  set  of  studding  can  be  removed  and  the  boards, 
not  being  nailed,  fall  out. 

Fig.  14  shows  a  method  where  the  boards  are  one  and  one-quar- 
ter to  one  and  one-half  inches  thick,  dressed  and  matched.  Be- 
cause of  the  tongue  and  groove  no  nails  whatever  are  required 
and  joints  may  be  broken  anywhere.  A  two  by  six  sill  is  laid  to 
start  and  this  is  set  with  an  instrument  and  secured  so  the  line 
can  be  maintained.  Studs  are  set  two  feet  apart  and  carefully 
plumbed  so  the  wall  will  be  truly  vertical.  Such  forms  are  readily 
kept  to  line  and  if  they  get  out  of  line  can  be  quickly  pulled  back. 
It  is  important  that  lines  be  kept  stretched  while  concrete  is  poured 
so  that  bulging  may  be  remedied  before  the  concrete  sets. 

The  boards  are  set  in  one  at  a  time  and  when  a  height  of 
about  eight  feet  is  reached  a  new  set  is  started.  The  longitudinal 
stringers  shown  with  bolt  heads  are  two  to  four  feet  apart  and 
the  upright  studs  are  lightly  fastened  to  them  with  small  nails 
merely  to  preserve  the  intervals.  The  bolts  run  through  the  walls 
independently  of  the  upright  studs  and  through  holes  in  the  boards. 
This  method  is  rapid  and  satisfactory  for  walls  not  very  thin. 

With  the  systems  of  forming  just  described  it  is  usual  to  have 
braces  against  the  lower  set  and  have  wire  ties  or  bolts  in  the 
higher  sets.  An  objection  to  braces  not  already  mentioned  is  that 
they  interfere  with  getting  close  to  the  walls  to  pour  unless  the 
pouring  is  done  from  a  considerable  height. 

Fig.  15  shows  a  panel  method  developed  by  Mr.  Ransome  and 
very  popular  for  thin  wall  work.  The  uprights  are  made  of  two 


84 


Reinforced  Concrete. 


pieces  of  two  by  four,  separated  at  each  end  by  blocks,  thus  form- 
ing slotted  braces.  To  start  a  wall,  spacers  the  thickness  of  the 
wall  at  the  bottom  are  set  on  the  ground  level  and  an  upright 
board  set  at  each  end.  On  the  outside  of  the  boards  are  placed 
sets  of  the  upright  slotted  frames  bolted  through  at  top  and  bot- 
tom and  with  a  spacer  at  the  top  equal  in  length  to  the  thickness 
of  the  wall  plus  the  thickness  of  the  two  boards. 


FIG.  15 — PANEL  METHOD. 

The  lower  bolt  is  slid  down  the  slot  until  it  rests  on  top  of 
the  boards  and  remains  there.  The  form  is  built  up  one  board  at 
a  time  until  the  upper  bolt  is  reached,  when  it  is  slid  down  to 
the  top  of  the  nearest  board  below  it.  The  building  up  is  con- 
tinued until  the  top  of  the  slotted  frames  is  reached,  when  the 
lower  bolt  is  withdrawn,  the  slotted  frames  moved  up  to  a  height 
as  great  as  may  be  obtained  when  the  upper  bolt  reaches  the  bot- 
tom of  the  slot.  The  lower  bolt  is  now  passed  through  the  upper 
part  of  the  slot,  with  a  new  spacer  there  to  preserve  the  interval, 
and  work  is  recommenced.  When  the  slotted  frame  is  moved  up 
the  boards  held  by  it  are  released  and  can  be  used  again  after 
cleaning. 


Other  Methods.  85 

Sometimes  the  slotted  frames  are  moved  up  oftener  than 
here  indicated.  Sometimes,  also,  instead  of  putting  in  one  board 
at  a  time,  panels  are  made  of  three  to  five  narrow  boards,  fastened 
together  by  cleats  on  the  back.  The  slotted  frames  are  seldom 
more  than  five  feet  long.  Panel  forms  of  this  kind  have  many 
points  of  weakness  about  them  on  account  of  the  joints,  unless 
care  is  taken  to  have  the  slotted  frames  lapping  over  the  ends  or 
to  have  two  frames  close  together  and  near  the  ends  of  their  re- 
spective panels.  The  amount  of  lumber  required  is  small  and 
thin  boards  may  be  used.  To  prevent  undue  deflection  a  great 
many  frames  must  be  used  with  thin  boards  and  this  means  con- 
siderable labor.  Each  panel  being,  to  a  certain  extent,  independent 
of  the  others  makes  it  extremely  difficult  to  keep  true  lines  with 
ordinary  care.  Men  become  expert  in  using  them  after  awhile 
and  as  they  require  less  material  and  skilled  workmanship  than 
any  other  style  of  forms  their  use  is  increasing.  With  such  forms, 
however,  it  is  found  as  with  others  that  every  endeavor  to  save 
material  results  in  an  increase  of  labor.  The  contractor  has,  there- 
fore, to  strike  a  balance  so  that  by  saving  lumber  he  can  use  such 
a  system  of  forms  that  the  lowest  paid  labor  can  be  employed  to 
advantage. 

Fig.  16  shows  another  panel  form  greatly  used.  Sometimes  a 
bolt  is  put  through  the  bottom  with  a  spacer  to  preserve  the  in- 
terval and  a  cleat  nailed  across  the  top.  The  panels  are  made 
about  three  feet  wide  and  can  be  of  any  length.  When  filled  to 
the  top  the  concrete  is  allowed  to  set.  The  form  is  then  raised  so 
the  bolt  rests  on  top  of  the  old  concrete  and  another  cleat  is 
nailed  across  the  top.  The  bottom  of  the  form  is  on  each  side  of 
the  concrete  already  poured  which  thus  acts  as  a  spacer. 

It  often  happens  with  concrete  work  that  work  cannot  pro- 
ceed with  such  regularity  that  the  forms  can  be  moved  one  at 
a  time,  for  some  concrete  sets  slowly.  Two  sets  of  forms  will 
then  be  used,  which  permits  of  one  set  being  left  in  place  while 
concrete  is  poured  in  the  set  above.  It  is  most  satisfactory  to 
have  three  sets.  The  bolts  have  large  washers  about  two  by  five 
inches  on  the  ends.  As  men  seem  to  be  very  slow  and  experience 
much  trouble  in  putting  the  bolts  through  the  bottom  of  the  forms 
it  is  convenient  to  put  them  through  the  top  with  a  spacing  cleat 
nailed  across  above  them.  This  cleat  is  of  course  knocked  off 
when  the  panel  is  filled.  When  the  panel  above  is  placed  the 
washer  is  turned  so  the  edge  of  the  frame  is  caught  and  thus 
one  bolt  serves  two  forms.  The  forms  are  generally  made  of  one- 


86 


Reinforced  Concrete. 


inch  boards   with   frames  of  two  by  four  stuff.     The   panels  are 
generally  made  with  the  upright  two  by  fours  two  feet  apart. 

The  last  mentioned  panel  forms  are  more  expensive  than  the 
slotted  frame  forms,  but  walls  made  with  them  can  be  kept  to 
line  as  well  as  walls  made  with  studding  set  up.  All  the  skilled 
labor  is  employed  in  making  the  panels  and  ordinary  men  can 
set  up  and  remove  them.  The  writer,  however,  has  had  a  job 
lately  where  the  setting  of  these  forms  seemed  beyond  the  ability 
of  ordinary  labor  and  the  men  who  were  on  the  pay  roll  as  car- 
penters killed  so  much  time  on  the  form  work  that  it  was  heart- 
breaking. So,  after  all,  the  costliness  of  any  particular  kind  de- 
pends very  much  upon  the  class  of  labor  employed  and  the  spirit 
it  is  possible  to  infuse  in  the  men. 


FIG.  16 — ANOTHER  PANEL  FORM. 

In  illustrations  on  pages  87  and  89  are  shown  several 
patented  methods  of  placing  forms  by  means  of  steel  clips  and 
fastenings  that  permit  of  the  use  of  one  board  at  a  time  and  no 
nails  or  uprights  are  required. 

The  writer  has  a  decided  preference  for  the  panelled  forms 
shown  in  Fig.  16  for  use  in  ordinary  thin  walls  of  reinforced  con- 


UNlVER3iTY   I 

OF  J 

^ 


Special  Forms. 


crete.  For  heavier  walls  and  especially  for  walls  not  reinforced 
the  system  shown  in  Fig.  14  is  his  favorite.  This  expression,  how- 
ever, is  to  be  modified  by  the  statement  already  made  referring  to 
cost  of  lumber  and  class  of  labor. 

For  long  walls,  not  much  broken  by  projections  or  recesses 
and  where  appearance  is  not  placed  high  above  most  other  con- 
siderations the  forms  shown  in  Fig.  11  can  be  used  to  advantage 
with  very  cheap  labor  and  poor  carpenters  and  the  forms  shown  in 
Fig.  15  can  be  used  with  cheaper  labor  and  no  carpenters.  The 
slotted  frames  can  be  made  at  a  planing  mill  or  carpenter  shop. 


FIG.  17 — SULLIVAN'S  PLANK  HOLDER. 

For  thick  walls  the  cost  of  forms  does  not  cut  much  figure 
and  can  be  kept  low,  per  cubic  yard  of  concrete,  so  that  any  of 
the  kinds  mentioned  can  be  used.  The  studding  and  boarded 
forms  made  in  place  will  generally  be  found  cheapest  and  most 
advantageous  in  every  way. 

When  walls  are  cut  up  at  close  intervals  by  pilasters  and 
counterforts  or  buttresses,  and  especially  when  such  walls  are  bat- 
tered, the  forms  shown  in  Fig.  16  will  be  the  cheapest  and  most 
satisfactory  to  use,  for  they  may  be  of  standard  lengths  and  the 
projections  can  be  formed  by  special  pieces.  Fig.  18  shows  special 
pieces  for  corners,  permitting  the  use  of  standard  length  forms. 

No  office  draughtsman  is  competent  to  design  any  reinforced 


88 


Reinforced  Concrete. 


ELEV/JT/ON. 


X) 

I 


EiEVffT/ON. 


PLAN. 
Oufa/de  corner. 


Ins/de  corner. 


FIG.   18 — CORNER   FORMS  FOR   BATTERED  WALLS. 


Special  Forms. 


89 


concrete  structure  out  of  the  ordinary  unless  he  has  had  actual 
construction  experience.  Forms  should  be  as  carefully  designed  as 
the  rest  of  the  details  of  actual  construction.  They  should  be  in- 
tended to  strike  a  happy  medium  between  economy  in  material 
and  economy  in  labor.  Forms  designed  with  a  view  to  only  one 
or  the  other  will  not  do.  It  is  well  to  design  forms  with  a  view 
to  re-use  if  possible  several  times. 


FIG.  19 — PARREL'S  PLANK  HOLDER. 

For  retaining  walls  all  the  foregoing  applies,  for  the  actual 
construction  work  is  the  same  for  all  walls.  For  sewers  and 
tanks,  panels  of  curved  shape  made  on  the  principle  of  the  panels 
shown  in  Fig.  16  must  be  used.  For  arches,  adaptations  of  the 
forms  in  Fig.  11  and  Fig.  16  are  used,  for  all  the  material  must 
remain  in  place  until  centers  are  struck. 


FIG.  20 — DIETRICH'S  PLANK  HOLDER. 

Draughtsmen  occasionally  send  out  designs  for  pier  and  column 
footings  showing  a  pyramidal  form.  Avoid  forms  of  such  shape 
for  they  will  invariably  float  and  it  is  next  to  impossible  to  fasten 


Reinforced  Concrete. 


FIG.    21 — THREE   STANDARD    METHODS   FOR    SECURING    COLUMN    FORMS. 


them  down.  Owing  to  the  difficulty  of  tamping  next  the  face 
they  will  be  rough  in  spite  of  all  work  done  to  assure  a  nice  face. 
The  writer  uses  for  footings,  frames  six  to  eight  inches  high. 
One  frame  is  put  down  and  filled.  While  the  concrete  is  still 
somewhat  soft  the  next  frame  is  put  in  place  and  filled,  so  pro- 
ceeding until  the  height  of  the  footing  is  attained.  The  frames 
are  then  removed  and  if  the  sloping  shape  is  insisted  upon  the 
steps  are  filled  with  stiff  mortar  trowelled  to  a  nice  finish.  Other- 
wise the  steps  remain. 

For  columns  it  is  customary  to  make  a   form  for  each  side 
anl  place  around  them  frames  of  two  by  fours  at  intervals  de- 


Columns  and  Beams. 


91 


cided  upon  by  the  pressure  to  be  resisted.  Bolts  are  run  through 
the  ends  of  the  pieces,  or  they  have  blocks  and  wedges.  Fig.  21 
illustrates  column  forms  in  general  use. 

Beams  and  girders  are  best  poured  in  forms  that  are  braced 
on  the  side  like  trusses.  Then  posts  can  support  these  forms  and 
framing  under  the  floor  panels  will  rest  on  the  lower  chords  of 
the  beam  and  girder  forms.  It  will  not  be  necessary  to  carry  sup- 
ports to  the  floor  underneath  to  carry  the  floor  or  roof  forms 
above.  This  means  a  tremendous  saving  in  lumber  for  bracing. 
It  also  means  a  saving  in  labor  for  removing  the  bracing.  The 
writer  knows  contractors  of  great  experience,  who  look  closely 
into  savings,  who  give  the  lumber  and  braces  used  under  floors 
to  any  one  who  will  remove  them,  if  the  material  has  to  be  passed 
out  of  narrow  or  small  openings.  When  this  material  is  cheaper 
than  the  labor  to  remove  it  some  thought  taken  in  saving  the 
amount  means  a  great  deal. 


FIG.    22 — BEAM   AND   FLOOR   FORMS,    ILLUSTRATING   METHOD  OF   TRUSSING   AND 
BRACING  TO   SAVE  .POSTS  UNDER  FLOORS. 

Simplicity  in  design  should  always  be  aimed  at  to  save  cost 
of  forms.  It  is  surprising  how  high  the  cost  can  be  when  the 
work  is  at  all  complicated.  When  walls  are  so  thick  that  spouts 
can  be  arranged  to  deliver  the  concrete  inside  the  reinforcement 
without  disturbing  it  then  high  forms  can  be  used.  Sometimes  as 
much  as  twenty  feet  can  be  poured  and  vertical  joints  instead  of 
horizontal  be  obtained.  In  such  walls  braces  may  be  preferable 
to  wires  or  bolts. 


92  Reinforced  Concrete. 

When  walls,  however,  are  thin  and  the  falling  concrete  cannot 
miss  the  steel,  it  is  risky,  to  say  the  least,  to  pour  more  than 
three  or  four  feet  at  the  most,  for  the  falling  concrete  may  dis- 
arrange the  steel.  If  high  forms  are  used  the  pouring  should  not 
stop  until  the  form  is  filled,  even  if  a  night  crew  is  put  on.  If 
this  is  not  attended  to  a  great  deal  of  concrete  will  adhere  to  the 
steel  and  to  the  sides  of  the  forms  and  get  dry.  When  pouring 
is  resumed  this  dry  stuff  will  be  knocked  off  and  falling  into  the 
fresh  concrete  will  make  a  bad  wall.  Some  of  it  will  still  cling 
to  the  steel  and  prevent  a  good  adhesion  of  the  newer  concrete  to 
the  reinforcement. 

In  erecting  forms,  building  lines  must  be  carefully  preserved 
by  means  of  strings  stretched  between  points  previously  accurately 
set  by  surveyor's  instruments.  Do  not  put  any  confidence  in  the 
ability  of  the  average  carpenter  to  carry  walls  vertically  with  a 
level.  The  plumbing  of  all  the  lines  should  be  done  by  a  few 
careful  men  and  the  rank  and  file  in  the  form  gang  should  be 
required  to  keep  the  lines  fixed.  Before  pouring  concrete  all 
forms  should  be  instrumentally  tested  for  position  and  horizontal 
and  vertical  alignment.  Warped  forms  should  be  rejected.  During 
the  pouring  of  the  concrete  there  should  be  men  at  hand  whose 
duty  it  shall  be  to  notice  when  forms  give  way  and  rectify  the 
trouble  at  once. 

The  finish  of  the  forms  depends  upon  the  degree  of  finish 
called  for  in  the  specifications.  If  matched  boards  are  not  used 
it  is  a  good  plan  to  chamfer  one  edge  of  the  boards  so  that  the 
joint  will  close  tightly  when  the  wood  is  wet.  If  cracks  open  more 
than  an  eighth  of  an  inch  the  forms  should  be  rebuilt. 

After  all  it  is  a  question  of  price  of  lumber  and  of  cost  and 
efficiency  of  labor.  When  lumber  is  high  in  price  small  panels  and 
shallow  pourings  will  be  the  rule.  When  lumber  is  cheap  deeper 
pourings  will  be  had  and  higher  panels.  The  man  who  ties  him- 
self to  one  standard  is  weak.  Interchangeability  is  good  and  an 
endeavor  should  be  made  to  standardize  the  work  as  much  as  pos- 
sible. Each  structure  must  be  a  special  study. 

The  construction  of  a  reinforced  concrete  structure  is  vastly 
different  from  that  of  a  plain  concrete  structure.  Reinforced  con- 
crete calls  for  a  richer  concrete  than  plain  concrete  work,  as 
strength  must  be  obtained.  In  many  situations,  however,  especially 
in  tank  walls,  mass  and  weight  often  accomplish  as  much  as 
strength  obtained  by  reinforcement.  Where  weight  will  do,  a  very 
cheap  concrete  can  be  used  in  heavy  walls  at  a  less  cost  than  with 
thin  reinforced  walls. 


CHAPTER  VII. 
THE  CONDUCT  OF  WORK. 

The  cement  used  for  reinforced  concrete  work  must  be  a  Port- 
land cement.  It  should  be  tested  in  order  to  insure  uniformity. 
It  should  be  used  directly  from  the  original  packages  as  received 
from  the  factory.  Batches  should  be  of  a  size  that  do  not  call 
for  parts  of  bags  or  barrels  as  no  exact  measurement  can  then 
be  made.  If  the  specifications  do  not  state  the  bulk  of  cement 
to  be  used  the  packed  barrel  or  packed  bag  must  be  used  as  the 
unit  and  the  size  of  the  unit  must  be  determined  by  the  engineer. 

Common  custom  now  makes  four  bags  equal  to  one  barrel 
of  cement,  and  in  bag  batches  one  bag  is  considered  equal  to 
one  cubic  foot.  This  is  about  a  mean  between  a  packed  foot 
and  a  moderately  loosened  foot  of  cement,  and  in  the  absence 
of  a  strict  definition  in  the  specifications  is  about  all  that  can 
be  insisted  on.  In  this  connection  the  writer  received  from 
Mr.  Robert  B.  Hansell,  C.  E.,  of  Baltimore,  the  following  table. 
The  sizes  of  cement  barrels  showed  such  variations  that  many 
tables  appeared  before  the  bags  came  into  common  use,  based  on 
barrels  containing  3.5,  3.8  and  4.0  cubic  feet.  This  table  shows 
the  number  of  cubic  feet  of  each  aggregate  based  on  one  cubic 
foot  per  bag. 

TABLE   X. 


Cu.  ft  per 
barrel  = 

3.5 

3.8 

4.0 

Proportions 

Bag 

Sand 
cu.  ft. 

Stone 
cu.  ft. 

Bag 

Sand 
cu.  ft. 

Stone 
cu.  ft. 

Bag 

Sand 
ft. 

Stone 
cu.  ft. 

1     3         5 

1 

10.5 

17.5 

1 

11.4 

19.0 

1 

12 

20 

1     2^     5 

1 

8.7 

17.5 

1 

9.5 

19.0 

1 

10 

20 

1     2         4 

1 

7.0 

14.0 

1 

7.6 

15.2 

1 

8 

16 

Two  mixtures  at  present  seem  to  be  in  general  use  for  rein- 
forced concrete  work.  For  work  requiring  concrete  of  consid- 
erable density  when  the  percentage  of  steel  is  high  a  1:2:4  mix- 
ture is  favored.  Taking  stone  and  sand  as  usually  received,  esti- 
mates for  purchasing  material  can  be  made  on  the  basis  of  six 


94  Reinforced  Concrete. 

bags  of  cement,  0.4  cubic  yards  of  sand  and  0.8  cubic  yards  of 
stone  for  each  cubic  yard  of  concrete.  For  the  greater  amount  of 
work  done  a  1 :3 :5  mixture  is  used.  This  will  call  for  4.5  bags 
of  cement,  half  a  yard  of  sand  and  0.8  cubic  yard  of  stone  per 
cubic  yard  of  concrete.  Rules  for  proportioning  concrete  materials 
abound,  but  after  all  none  are  exact,  for  an  exact  determination  of 
quantities  depends  upon  the  percentage  of  voids  in  the  stone  and 
sand.  A  rule  credited  to  Mr.  Fuller,  used  by  many  contractors,  is 
to  add  the  proportions  together  and  divide  11  by  the  sum.  For 
example  the  sum  of  1 :2 :4  is  7.  Eleven  divided  by  7  gives  1.58, 
the  number  of  barrels  of  cement  per  cubic  yard.  The  barrel  of 
cement  in  this  rule  contains  3.8  cubic  feet.  Multiplying  the  two 
numbers  together  gives  1.58x3.8=6  bags  of  cement.  For  sand, 
6x2=12  cubic  feet,  or  0.45  cubic  yard,  and  for  stone  6x4=24  cubic 
feet,  or  0.9  cubic  yard.  This  rule,  it  is  understood,  was  obtained 
by  taking  the  number  of  barrels  of  cement  known  to  have  been 
used  on  very  large  works,  together  with  the  number  of  cubic 
yards  of  sand  and  stone,  and  ascertaining  the  number  of  cubic 
yards  of  concrete  made.  It  is  necessarily  very  general,  but  allows 
liberally  for  waste  and  is  safe  enough  for  ordinary  jobs.  For  close 
competition  the  voids  should  be  ascertained  and  careful  calcula- 
tions made. 

All  concrete  for  reinforced  work  should  be  mixed  by  machine. 
This  rule  is  imperative.  If  hand  mixing  is  required  in  an  emer- 
gency the  inspector  should  pay  the  closest  possible  attention  to  it. 
It  should  be  done  carefully  and  with  due  deliberatoin.  All  hurry 
that  smacks  of  haste  should  be  avoided.  The  ordinary  methods 
good  enough  for  mass  work  cannot  be  tolerated.  The  sand  and 
cement  should  first  be  mixed  until  the  color  is  uniform  and  no 
streaks  show.  A  minimum  number  of  turns  should  be  six  after 
spreading  the  cement  first  carefully  over  the  sand.  Then  the 
water  should  be  added  gently  through  a  rose  nozzle.  A  minimum 
number  of  turns  during  this  operation  is  four  and  one  set  of  turn- 
ings should  not  be  considered  sufficient  to  mix  the  sand  and  cement 
and  at  the  same  time  apply  the  water.  When  the  mixing  is  done 
the  paste  should  be  somewhat  thick.  The  stone  must  be  previously 
wetted  and  when  the  paste  is  ready  thrown  into  it  and  the  whole 
mass  quickly  turned  until  all  the  stone  is  covered  with  cement 
paste.  Water  will  be  added  until  the  concrete  is  of  the  right 
degree  of  plasticity.  For  this  final  mixing  with  stone  a  minimum 
number  of  turns  will  be  four. 

No  matter  what  the  directions  of  the  makers  no  batch  of  con- 


Mixing  and  Measuring.  95 

crete  should  be  given  less  than  twenty  turns  in  the  mixer.  If  a 
mixer  of  the  continuous  delivery  type  is  used  the  length  of  the 
trough  should  permit  a  number  of  turns  equivalent  to  twenty  turns 
per  batch  or  should  be  so  arranged  that  the  mass  can  be  held  in 
place  until  it  receives  such  turning.  In  continuous  feed  machines 
the  cement  is  apt  to  clog  so  the  cement  feed  should  be  closely 
looked  after.  Several  tests  should  be  made  each  day  to  see  that 
the  cement  delivery  is  constant. 

The  writer  wishes  to  state  as  a  result  of  his  own  experience 
that  it  pays  to  equip  a  mixer  with  charging  apparatus  to  reduce 
the  number  of  men  wheeling  stone  and  sand.  With  a  batch  mixer 
it  is  well  to  have  a  super  hopper  containing  one  batch  in  reserve. 
In  addition  there  should  be  an  elevating  hopper  which  can  be 
loaded  on  the  ground  level  by  men  and  do  away  with  inclines. 
While  a  batch  is  being  mixed  there  is  one  in  reserve  in  the  super 
hopper  and  another  being  placed  in  the  charging  hopper.  It  will 
reduce  the  number  of  men  required  by  two-thirds  in  charging  alone. 
Charging  hoppers  generally  have  a  steel  diaphragm,  on  one  side  of 
which  the  sand  is  placed  and  on  the  other  the  stone.  The  measur- 
ing is  thus  to  a  certain  extent  automatic.  When  the  hopper  is 
discharged  into  the  super  hopper  a  fair  mix  is  obtained.  The 
cement  can  be  added  while  the  charge  is  in  the  super  hopper  and 
when  the  materials  run  into  the  mixing  drum  another  fair  mix  is 
obtained.  This  tends  to  lessen  the  time  required  for  actual  mixing. 

When  materials  are  delivered  by  wheelbarrows  the  incline 
should  be  easy.  When  starting  the  work  place  the  mixer  as  low 
as  possible  and  send  the  material  down  through  a  chute  to  the 
bottom  of  the  work.  As  the  walls  rise  the  chute  can  be  shortened 
until  the  work  reaches  the  height  of  the  mixer.  Then  the  mixer 
can  be  raised  until  the  incline  is  as  steep  as  men  can  work  on. 
After  that  a  hoisting  elevator  of  some  sort  should  be  used  to 
take  the  concrete  to  the  elevation  where  wanted.  A  concrete  hoist 
is  a  good  investment  if  the  concrete  has  to  be  elevated  more  than 
ten  feet. 

Measuring  stone  and  sand  by  wheelbarrows  is  simply  guessing 
and  should  not  be  tolerated.  The  illustration  shows  a  form  of  box 
used  by  the  writer.  The  length  and  widths  given  fit  the  average 
concrete  wheelbarrow.  The  height  of  course  depends  upon  the 
size  of  load  wanted.  The  boxes  are  bottomless  and  are  placed 
in  the  wheelbarrow  and  filled  flush  to  the  top.  It  is  easy  to  lift 
them  by  the  handles  and  the  material  drops  out.  By  using  such 
boxes  exactness  and  uniformity  can  be  attained  in  proportioning 


96 


Reinforced  Concrete. 


the  ingredients.  The  ordinary  wheelbarrow  is  said  to  hold  three 
cubic  feet.  This  means  three  cubic  feet,  water  measure,  when  the 
wheelbarrow  is  held  in  such  a  position  that  the  water  exactly 
touches  all  the  edges.  If  left  to  themselves  the  men  will  not  load 
much  more  than  two  feet  and  seldom  load  with  as  much  as  two 
feet.  When  driven  hard  they  will  carry  much  more  and  the  lack 
of  uniformity  is  bad. 

;*j  I/I          ' 

-*--! I7f-    -    -    --;.;  ' 


FIG.  23 — MEASURING  Box. 

Concrete  must  be  wet  enough  to  flow  readily  around  and 
cover  the  steel,  but  must  not  be  thin  and  watery.  The  ideal  mix- 
ture is  one  that  will  not  slip  too  readily  from  the  wheelbarrow  or 
cart  and  is  best  described  by  the  word  "pasty."  It  should  be  as- 
sisted out  by  a  shovel. 

Thin  concrete  is  discharged  more  rapidly  from  the  mixer  and 
is  consequently  favored.  The  water,  however,  during  the  setting 
and  seasoning  process  leaves  the  concrete  porous  if  too  thin  when 
poured.  Speed  in  operating  a  mixer  depends  largely  upon  the 
amount  of  water  pressure  available  and  it  pays  to  insure  a  good 
pressure  even  if  an  elevated  tank  must  be  put  up  when  the  pres- 
sure in  the  city  mains  is  low.  Measuring  the  water  is  best  done  by 
an  experienced  man  with  good  judgment.  It  simply  requires 
training  and.  such  a  man  is  better  than  the  best  automatic  device 
ever  invented,  except  of  course  for  very  large  mixers.  After  a 
rain  the  sand  and  stone  contain  so  much  water  that  the  amount 
used  must  vary  with  each  batch.  In  dry  summer  weather  more 
water  must  be  used  than  in  wet,  cool  weather. 


Placing  the  Concrete.  97 

The  importance  of  using  plenty  of  water  in  dry  weather 
should  be  impressed  upon  workmen.  This  water  should  not 
all  be  added  in  the  mixer.  In  hot  weather  the  stone  and  sand 
pile  should  be  wet,  precisely  as  brick  masons  wet  brick,  and  for 
the  same  reason.  The  stone  may  be  of  a  kind  that  will  absorb 
water  rapidly  and  interfere  with  the  proper  setting  of  the  cement 
next  to  it. 

The  concrete  must  be  worked  to  the  face  of  the  forms  to  in- 
sure a  good  surface  and  must  be  well  worked  into  all  interstices 
to  insure  a  good  job.  The  methods  used  must  be  those  calculated 
to  best  secure  the  desired  results.  Heavy  tamping  is  not  neces- 
sary with  pasty  concrete  and  is  apt  to  displace  the  forms.  What 
is  wanted  is  something  that  will  insure  every  piece  of  stone  being 
thoroughly  imbedded  in  the  mass  and  also  see  that  all  the  steel 
is  surrounded  and  that  none  is  displaced.  All  air  must  be  released 
so  far  as  that  is  possible.  Churning  with  rods  and  pipes  is  good. 
A  piece  of  one  by  three  wood  is  as  good  as  anything  when  the 
lower  end  is  sharpened  and  fixed  like  a  butter  paddle. 

The  concrete  must  be  worked  back  from  the  forms  and  many 
tools  are  used  by  different  men — wooden  paddles  as  above, 
potato  forks  and  manure  forks  with  curve  taken  out.  There 
are  several  special  concrete  spades  on  the  market  also.  The  writer 
uses  wood  and  also  slicers  and  spades  made  with  handles  seven 
feet  long  of  three-quarter-inch  pipe,  having  on  the  end  a  piece  of 
sheet  steel  one-eighth  of  an  inch  thick,  ten  inches  long  and  with  a 
width  at  the  lower  end  of  four,  six  and  eight  inches.  That  is,  the 
three  widths  are  used  on  the  job.  The  narrower  ones  are  very 
handy  for  cleaning  forms.  Churning  with  rods  is  so  good  that  a 
number  of  men  should  be  kept  at  it 

In  pouring  columns  or  filling  forms  exceeding  three  feet  in 
height  the  directions  given  in  the  chapter  on  columns  should  be 
carefully  followed. 

To  assist  in  obtaining  a  dense,  impervious  concrete  for  floors 
and  roofs  a  wooden  float  about  ten  or  twelve  inches  wide  and  not 
less  than  four  feet  long  should  be  used  as  a  tamper,  two  men  con- 
tinually tamping  with  same  to  consolidate  the  mass  and  help  draw 
the  cement  to  the  surface.  There  has  lately  been  placed  on  the 
market  a  tamper  for  floor  surfaces  consisting  of  flat  bars  ar- 
ranged like  a  grating.  These  bars  cut  down  into  the  concrete  and 
do  the  work  the  stirring  rods  do  in  wall  forms.  The  usual  top 
coat  and  finish  can  be  applied  within  the  customary  time. 

Particular  care  must  be  exercised  to  see  that  steel  is  not  dis- 


98  Reinforced  Concrete. 

placed  when  pouring  concrete.  Occasional  tapping  or  pounding  on 
the  forms  as  they  are  filled  helps  the  flow  of  the  concrete  around 
the  steel  and  prevents  to  some  extent  the  lodging  of  stones  in 
such  positions  that  a  rod  or  bar  may  be  permanently  displaced. 

Unless  prevented  by  accident,  beams  and  girders  should  be 
poured  with  the  floors,  regardless  of  design.  If  designed  as  T 
sections  this  rule  is  imperative  and  no  accident  can  be  an  excuse 
for  not  doing  it.  Beams  and  girders  of  T  section  are  designed 
for  economy.  The  economy  is  usually  all  on  paper.  The  design  of 
T  beams  has  been  discussed  in  Chapter  I.  There  are  times 
often  when  it  is  an  absolute  impossibility  to  pour  the  beams  and 
slab  at  one  operation  and  complete  the  work.  To  stop  properly 
would  require  that  a  stop  be  placed  in  the  center  of  the  beam, 
running  its  entire  length  and  going  clear  to  the  bottom.  This 
makes  in  effect  two  narrow  beams.  Practically  this  is  an  impos- 
sibility owing  to  the  presence  of  the  reinforcement,  so  the  work 
is  stopped  somewhere  on  the  beam  with  a  small  ledge  left  on 
which  to  rest  the  beginning  of  slab  work  the  next  day.  With 
the  class  of  labor  usually  to  be  had  one  cannot  always  stop  where 
theoretically  he  should,  so  there  is  always  more  or  less  of  a  ques- 
tion about  the  job.  There  are  days  when  it  makes  no  difference 
but  the  days  occur  so  frequently  when  there  is  a  difference,  that 
one  is  safest  in  so  designing  that  if  considered  advisable  all  the 
beams  and  girders  may  first  be  poured  and  the  floor  later. 

The  steel  must  be  correctly  placed  and  all  the  steel  must  go 
in.  This  is  imperative.  The  work  is  designed  with  the  steel  cal- 
culated to  occupy  a  certain  definite  position.  To  the  extent  that  a 
bar  or  rod  deviates  from  its  proper  position  to  that  extent  the 
work  is  defective.  Wherever  rods  or  bars  cross  they  should  be 
wired  together  securely.  No.  18  wire  is  the  best.  The  writer 
uses  it  cut  into  lengths  of  about  eight  inches  and  generally  has 
the  men  use  two  of  such  pieces  at  each  intersection.  This  has 
already  been  mentioned.  Several  parties  have  written  to  the  writer 
saying  it  was  not  necessary  to  be  so  finicky  and  that  the  wiring 
was  too  expensive!  The  only  reply  possible  to  such  critics  is 
that  the  structure  must  be  erected  as  designed  and  it  is  not  possi- 
ble to  so  erect  it  unless  the  steel  is  actually  occupying  the  position 
intended.  The  writer  has  seen  contractors  placing  steel  in  a  hurry 
ahead  of  a  concreting  gang.  He  has  seen  it  displaced  and  very 
irregular  and  confesses  he  does  not  like  it.  He  has  seen  floors 
with  steel  all  in,  according  to  the  superintendent,  that  called  for 
twenty  per  cent  more  bars  after  they  were  regularly  spaced  and 


Placing  the  Steel.  99 

wired.  Wiring  is  expensive,  else  experienced  men  would  not  use 
ready  fabricated  materials  at  the  high  prices  charged  for  them. 
These  fabrics  sell  readily  because  they  do  not  cost  much  to  place 
and  when  placed  it  is  a  great  comfort  to  know  that  every  strand 
is  where  the  designer  wanted  it. 

Lastly  it  must  be  taken  into  consideration  that  the  height  from 
which  concrete  can  be  poured  depends  to  a  great  extent  upon  the 
security  with  which  the  steel  is  fastened  together.  So  it  must  be 
wired  to  get  it  to  the  place  it  belongs  and  to  keep  it  there  during 
construction. 

It  is  not  difficult  to  place  steel  in  walls  and  keep  it  the  right 
distance  from  the  face.  With  flat  slabs  however  it  is  different. 
Some  provision  must  be  made  to  insure  a  flow  of  concrete  under 
the  bars.  Some  contractors  have  men  ahead  of  the  wheelbarrow 
gang  hastily  prying  up  the  mat  to  allow  the  mortar  to  flow  under. 
Others  use  small  pieces  of  steel  under  the  bars  to  hold  them  up, 
which  are  consequently  imbedded  and  show  on  the  underside. 
Others  use  small  blocks  of  concrete  broken  from  thin  slabs  made 
for  the  purpose.  Some  use  regular  concrete  supports  made  for  the 
rods  used  and  others  use  a  recently  patented  chair  of  thin  steel 
which  acts  also  as  a  clip  and  saves  the  expense  of  wiring.  The 
writer  has  used  them  all  and  also  uses  a  method  which  is  about 
as  satisfactory  as  any.  He  places  lines  of  two  by  fours  about 
four  or  five  feet  apart  over  the  floor  and  suspends  the  reinforcing 
mat  from  them  by  wires.  The  supports  for  the  timbers  serve  also 
as  supports  for  running  plank.  Thin  mortar  is  first  poured  to  a 
depth  of  about  an  inch  when  the  wires  are  cut  and  the  steel  drops 
into  the  mortar.  The  timbers  and  their  supports  are  removed  and 
the  concrete  rushed  in  on  running  plank  laid  on  the  steel. 

Opinions  and  practice  differ  on  the  subject  of  the  thin 
mortar  coat  placed  on  the  floor,  into  which  the  steel  is  allowed 
to  drop.  It  costs  less  and  is  quicker  work  when  concrete  is 
poured  first  along  one  side  of  the  floor  and  the  concrete  after 
that  is  poured  on  the  concrete  so  that  the  thin  mortar  flows 
away  from  it  and  under  the  steel.  This  makes  it  unnecessary 
to  first  mix  batches  of  mortar,  with  the  attendant  annoyance 
and  delay  and  going  over  the  floor  twice.  The  only  objection 
to  the  method  of  pouring  on  the  advancing  edge  and  letting 
the  mortar  flow  ahead  under  the  steel  is  that  the  steel  may  not 
always  drop  as  far  as  it  should,  so  that  some  may  be  held 
nearer  the  neutral  axis  than  is  right.  With  an  experienced  crew 
and  careful  boss  who  does  not  rattle  the  men  by  hurrying  them, 


100 


Reinforced  Concrete. 


any  method  is  good,  and  this  method  of  dispensing  with  the 
first  coat  of  thin  mortar  is  excellent.  The  floor  forms  should  be 
soaked  with  water  before  pouring  concrete. 

Steel  placed  in  beams  and  girders  should  be  suspended  in 
some  way  until  mortar  can  "be  placed  under  and  around  it.  In 
fact  no  harm  is  done  if  the  beam  is  filled  half  way  to  the  neutral 
axis  in  order  to  set  and  retain  the  steel  in  place.  Care  must  be 
taken,  however,  to  insure  a  good  joint  when  the  pouring  is  com- 
pleted. If  the  beam  is  one  that  will  show,  such  a  proceeding  is  not 
possible  for  the  line  between  the  two  pourings  will  be  well  defined. 

Care  must  be  taken  that  forms  are  secure,  either  by  wiring, 
bolting  or  bracing. 

The  writer  has  computed  some  tables  for  his  own  use  con- 
sidering that  concrete  will  exert  a  pressure  equal  to  a  fluid  weighing 
eighty  pounds  per  cubic  foot. 

The  first  table  shows  the  pressure  per  square  foot  at  different 
depths  and  the  pressure  on  a  strip  one  foot  wide  for  the  heights 
indicated.  The  second  table  gives  the  spacing  vertically  for  wires 
and  bolts  and  a  comparison  is  afforded  between  wires  of  different 
gauges  and  bolts  of  different  diameters.  This  gives  the  user  an 
opportunity  to  take  whatever  the  market  can  give.  The  horizontal 
distances  are  twenty-four  inches,  the  vertical  spacing  alone  varying. 
For  example  if  a  form  six  feet  high  is  poured  it  will  require 
twenty-five  ties  of  No.  18  wire  with  intervals  as  shown,  or  ten 
wires  of  No.  14,  or  only  three  of  No.  9.  The  wires  to  be  doubled, 
as  shown  in  drawing,  and  twisted. 

TABLE   XL 
PRESSURE  OF  FRESH  "SOUPY"  CONCRETE. 


Depth  in  feet 

•n 

i!1 

&<>-« 

11 
U 

£rH 

Depth  in  feet 

Pressure  on 
Vertical  Strip 
1  Foot  Wide. 

i 
t 

It 
U  . 

H«-« 

Depth  in  feet 

• 

c£§ 

m 

m 
&* 

§§ 

g£ 
jjj? 

1 
2, 
3 

4 
5 
6 

7 
8 

40 
160 
360 
640 
1,000 
1,440 
1,960 
2,560 

80 
160 
240 
320 
400 
480 
560 
640 

a 

10 

11 

12 
13 
14 
15 
16,    . 

3,240 
4,000 
4,840 
5,760 
6,760 
7,840 
9,000 
14,240 

720 
800 
880 
960 
1,040 
1,120 
1,200 
1,280 

17 
18 
19 
20 
21 
22 
23    . 
24    , 

11.560 
12,960 
14,440 
16,000 
17,640 
19,360 
,  21,160 
23,044 

1,360 
1,440 
1,520 
-1,600 
1,680 
1,760 
1,840 
1,920 

Wire  and  Bolts. 


101 


TABLE   XII. 

WIRE  AND  BOLT  TABLE  FOR  CONCRETE: 

Showing  vertical  intervals,  measuring  from  the 
cure  forms.    Horizontal  spacing,  two  feet    Wires  do 


to  se- 


• 

«" 

SIZES  01 

X" 

r  BOLTS. 
H" 

ys 

8 

I 

GAUf 

10 

;B  or  w 
12 

IRE. 
14 

16 

18 

ftin. 

ftin. 

ft.in. 

ft.in. 

ftin. 

ftin. 

ft.in. 

fUn. 

ft.in. 

ftin. 

ftin. 

8  6 
12  6 
15  0 
17  6 
19  6 

21  6 
23  3 
24  6 

*:::: 

'f.  ... 

6  6 
9  6 
12  0 
14  0 
16  0 

17  6 
18  8 
1910 
21  0 
22  0 

23  0 
24  0 
25  0 

5  0 
7  6 
9  0 
10  6 
11  » 

13  0 
14  0 
14  9 
15  6 
•16  3 

17  '0 
17  9 
18  6 
19  3 
20  0 

2.0  8 
21  4 
22  0 
22  6 
23  0 

23  6 
24  0 
24  6 
25  0 

3  6 
5  0 
6  0 
7  0 
8  0 

8  6 
9  0 
9  6 
10  0 
10  6 

11  0 
11  6 
12  0 
12  6 
13  0 

13  6 
14  0 
14  5 
14  10 
15  -3 

15  8 
16  0 
16  4 
16  8 
17  0 

17  4 

17  8 

3  6 
5  6 
6  6 
7  6 

8  0 

9  « 
10  3 
11  0 
11  9 
12  6 

13  0 
13  '6 
14  0 
14  6 
15  0 

15  6 

16  0 
16  6 
17  0 
17  4 

17  8 
18  0 
18  4 
18  8 
19  0 

19  4 
19  8 

3  6 
5  0 
6  0 
7  0 
8  0 

9  0 
9  6  • 
10  0 
10  6 
11  0 

11  6 
12  0 
12  6 
13  0 
13  6 

14  0 
14  6 
15  0 
15  6 
16'0 

16  4 
16  8 
17  0 
17  4 
17  g 

18  0 

3  0 
4  0 
5  0 
6  0 

2  0 
3  0 
4  0 

5  0 

2  0 
2  8 
4 

0 

0 
0 
6 
0 

0 

0 

10 
0 

1 

1 
1 

510 
611 

«  0 

8  0 

.8  6 
9  0 
9  6 
10  0 

10  6 
11  0 
11  6 
12  0 
12  6 

13  0 
13  4 
13  8 
14  0 
14  4 

14  8 
15  0 
15  4 
15  8 
16  0 

6  0 
6  6 
7  0 
7  6 
8  0 

8  4 
8  S 
9  0 
9  4. 
9  8 

10  0 
10  4 
10  8 
11  0 
11  -4 

11  8 
12  0 
12  3 
12  6 
12  9 

13  0 

8 
0 
4 

8 
0 

6  4 

6  8. 

^r°s 
.7  e 

•7  9 
8  0 
8  3 
8  6 
8  8 

810 
.00 
9  3 
9  6 
9  8 

910 
10  0 

8 
0 
3 
6 
0 

0 
3 
6  6 
6  8 
510 

6  0 
62 
6  4 

6  6 

8  8 

610 
7  0 
7  4 
7  7 
7  9 

711 
8  0 

.... 

.... 

.... 

.... 



.... 

Wt.  pe 

1.6'43 

r  Foot  ( 
.668 

)f  Rods, 
.  .376' 

Ibs.  . 
.167 

Feet  per  Pound. 
14.29  |  17.05  |  20.27  ['  33.69  |  58.58  |  95.98  1  166.20 

The  third  table  gives  the  total  load  in  pounds  for  columns, 
struts  or  braces  having  lengths  varying  by  single  feet.  If  the 
brace  is  placed  at  an  angle  of  forty-five  degrees  the  length  will 
be  1.41  times  the  height  from  the  ground  to  the  top  of  the  brace. 
For  convenience  in  mentally  estimating  the  length  it  is  called  1.5 
times  the  height.  From  the  first  table  the  pressure  at  any  point 
can  be  ascertained  and  thus  the  load  to  be  carried  by  the  brace. 
Looking  in  the  third  table  for  braces  of  the  required  length  the 
load  can  be  found  on  the  same  line  and  at  the  top  of  the  column 
in  which  this  load  is  found  will  be  found  the  size  of  brace  re- 
quired. This  table  is  also  useful  for  putting  supporting  posts  and 
studding  under  floor  forms.  The  loads  are  for  ordinary  white 


102 


Reinforced  Concrete. 


TABLE  XIII. 


SAFE  LOADS  FOR  POSTS  AND  BRACES  (Common  Pine). 


Lengths 
in  Feet 

2x4 

2x6 

Sizes 
2x8  |  8x4 

in  Inches. 
4x4  |   4x6  |  6x6 

6x8  |   8x8 

Load  in  pound*. 

1 
2 

8 

4 

6 
7 
8 
9 
10 

11 
12 
18 
14. 
IB. 

19 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26, 
27 

28. 

4,800 
4,136 
8,648 
8,860 

8,072 
2,784 

2,496 
2,208 
1,920 

1,632 
1,344 
1,056 
768 
480 

192 

7.200 
5,904 
5,472 
6,040 

4,608 
4,176 
8,744 
3,312 
2,880 

2,448 

2,016 
1,584 
1,152 
720 

288 

9,600 
8,272 
7,296 
6,720 

6,144 

5,568 
4,992 
4,416 
8,840 

8,264 

2,688 
2,112 
1,536 
060 

884 

7,200 
6,048 
5,760 

6,472 
6,184 
4,896 
4,608 
4,820 

4,032 
8,744 
3,456 
3,168 
2,880 

2,592 
2,304 
2,016 
1,728 
1,440 

1,152 
864 
576 
288 

9,600 
8,160 

7,872 
7,584 
7,296 
7,008 
6,720 

6,432 
6,144 
6,856 
5,568 
5,280 

4,992 
4,704 
4,416 
4,128 
8,840 

8,552 
3,264 
2,976 

2,688 
2,400 

2,112 
1,824 
1,536 

14,400 
12,240 

11,808 
11,376 
10,944 
10,512 
10,080 

9,648 
9,2  1* 
8,784 
8,352 
7,920 

7,488 
7,056 
6,624 
6,192 
6,760 

6,328 
4,896 
4,464 
4,032 
3,600 

8,168 
2,736 
2,304 

21,000 
18,576 
18,144 
17,712 
17,280 

16,848 
16,416 
15,984 
15,552 
15,120 

14,688 
14,256 
13,824 
13,392 
12,960 

12,528 

12,096 
11,664 
11,232 
10,800 

10,868 
9,936 
9,504 

28,800 
24,768 
24,192 
23,616 
23,040 

22,464 

21,888 
21,312 
20,736 
20,160 

19,584 

19,008 
18,432 
17,856 
17,280 

16,704 
16,128 
15,552 
14,976 
14,400 

13,824 
13,248 
12,672 

38,400 
88,280 

82,768 
82,256 
81,744 
81,282 
80,720 

80,208 
29,696 
29,184 
28,672 
28,160 

27,648 
27,186 
26,624 
26,112 
25,600 

25,088 
24,576 

24,064 

TABLE  XIV. 

THICKNESS  OF  HORIZONTAL  BOARDS  FOR  FORMS. 
VERTICAL   STUDDING,  2x4  INCHES. 


Thickness 
of 
Boards, 
inches. 

Studding  Intervals. 
12"       |       18*       |       24* 

.    It  is  assumed  all  boards  are 
1A   in.  less  thickness  than  here 
given. 
Studding  is  assumed  to  be  suf- 
ficiently braced  or  tied; 
As    heights   of   form   increase 
use  thicker  boards  at  bottom  or 
set  studding  closer. 

Height  of  Forms  —  Feet 

1 

iCZ 

.t* 

21 
28 
89 

8 

6J4 
10  V* 
12*4 
1854 

.* 

5* 
9 
12 

Spikes  and  Nails. 


103 


pine  or  spruce.  For  yellow  pine  (southern)  the  loads  may  be 
thirty  per  cent  greater  and  for  white  oak  twenty  per  cent. 

The  following  table  shows  the  spans  that  may  be  used  for 
boards  of  different  thickness.  This  is  assuming  that  studding  is 
used  vertically  and  the  boards  are  nailed  or  held  in  some  way 
against  them  horizontally,  the  uprights  being  secured  by  wires, 
bolts  or  braces. 

The  following  tables  containing  the  strength  of  beams  one 
inch  thick  and  giving  sizes  of  nails  and  spikes  and  weights  of 
nut  and  bolt  heads  are  from  the  Carnegie  Pocket  Book  and  will 
be  useful  in  ordering  material  for  forms. 

TABLE    XV. 
SPIKES  AND  NAILS. 


Standard  Steel  Wire  Nails 

Steel  Wire  Spikes 

Comgogl™ 

.1 

is 

Common 

Finishing 

8 

11 

Si 

| 

n 

s 

|I 

Diam. 
Ins. 

No. 
per  Ib. 

Diam 
Ins. 

No. 
per  Ib. 

2d 

1 

.0524 

1060 

.0453 

1558 

3 

.1620 

41 

Id 

800 

3d 

i  J4 

.0588 

640 

.0508 

913 

3V4 

.1819 

30 

3d 

J4 

400 

4d 

i  J4 

,0720 

380 

.0508 

761 

4 

.2043 

23 

4d 

Q 

800 

N 

i& 

.0764 

275 

.0571 

500 

.2294 

17 

5d 

3£ 

200 

6d 

2 

.0808 

210 

.0641 

350 

•5 

.2576 

13 

6d 

150 

7d 

2  J4 

.0858 

160 

.0641 

315 

.2893 

11 

7d 

lA 

120 

8d 

2  V* 

.0935 

115 

.0720 

214 

Q 

.2893 

10 

N 

D 

85 

9d 

2J4 

.0963 

93 

.0720 

195 

en 

.2249 

7*4 

9d 

J4 

75 

lOd 

3 

.1082 

77 

.0808 

137 

7 

.2249 

7 

lOd 

60 

354 

.1144 

60 

.0808 

127 

8 

.3648 

5 

12d 

54 

50 

16d 

3V5 

.1285 

48 

.0907 

90 

9 

.3648 

16d 

l/2 

40 

20d 

4 

.1620 

31 

.1019 

62 

SOd 

4 

20 

80d 

.1819 

22 

30d 

«K 

16 

40d 

5 

.2043 

17 

40d 

I 

14 

60d 

.2294 

13 

SOd 

n 

60d 

6 

.2576 

11 

60d 

6 

8 

WROUGHT  SPIKES. 

Number  to  a  Keg  of  150  Ibs. 


Length 
Inches 

%?• 

Vo- 

*V£ 

Length 
Inches 

«£ 

MS: 

Vo"" 

%"• 

*& 

lit 
\« 

6 

2250 
1890 
1650 
1464 
1380 
1292 

1208 
1135 
1064 
930 
868 

'742 
570 

7 
8 
9 
10 
11 
12 

1161 

662 
635 
673 

482 
455 
424 
391 

445 
384 
300 
270 
249 
236 

806 
256 
240 
292 
208 
180 

—Carnegie  Pocket  Book, 


104 


Reinforced  Concrete. 


TABLE    XVI. 

SAFE  LOADS  UNIFORMLY  DISTRIBUTED  FOR  REC- 
TANGULAR SPRUCE  OJfc  WHITE  PINE  BEAMS 
ONE  INCH  THICK. 

The  following  table  has  been  calculated  for  extreme  fiber 
stresses  of  750  Ibs.  per  square  inch  corresponding  to  the  follow- 
ing values  for  Moduli  of  Rupture  recommended  by  Prof.  Lanza, 
viz.: 

Spruce  .and  white  pine . 3,000  Ibs. 

Oak 4,000  Ibs, 

Yellow  pine 5,000  Ibs. 

For  oak  increase  values  in  table  by  Y$.  For  yellow  pine 
increase  values  in  table  by  ^. 

The  safe  load  for  any  other  values  per  square  inch  is  found 
by  increasing  or  decreasing  the  loads  given  in  the  table  in  the 
same  proportion  as  the  increased  or  decreased  fiber  stress. 


Span 
in 
Feet 

6 

7 

8 

Dl 
9 

,PTH  OP 
10 

BEAM- 
11 

—  IN  CHE 
13 

s. 
13 

14 

16 

Id 

6 

.600 

820 

1,070 

1,350 

1,670 

2,020 

2,400 

2,820 

3,270 

3,750 

4,270 

6 
7 

}  600 

.430 

680 
580 

890 
760 

1,120 
960 

1,390 
1,190 

1,680 
1,440 

2,000 
1,710 

2,350 
2,010 

2.730 
2,330 

3,120 

2,680 

8,560 
3,050 

8 

.380 

510 

670 

840 

1,040 

1,260 

1,500 

1,760 

2,040 

2,340 

2,670 

0. 

,830 

460 

590 

750 

930 

1,120 

1,330 

1,560 

1,810 

2,080 

2,370 

10 

.800 

410 

630 

670 

830 

1,010 

1,1500 

1,410 

1,630 

1,880 

2,130 

11 

.270 

370 

490 

610 

760 

920 

1,090 

1,280 

1,490 

1,710 

1,940 

12, 

.250 

340 

440 

660 

690 

840 

1,000 

1,180 

1,360 

1,560 

1,780 

.13. 

.230 

310 

410 

620 

640 

780 

930 

1,080 

1,260 

1,440 

1,640 

14 

;21t) 

290 

380 

480 

590 

720 

860 

1,010 

1,170 

1,340 

1,630 

15 

'.200 

270 

360 

450 

660 

670 

800 

940 

1,090 

1,250 

1,420 

16 

.190 

260 

330 

420 

620 

630 

750 

880 

1,020 

1,180 

1,330 

17 

.180 

240 

310 

400 

490 

690 

710 

830 

960 

1.  WO 

1,260 

18 

.170 

230 

290 

870 

460 

660 

670 

780 

910 

1,040 

1,190 

19 

.160 

210 

280 

860 

440 

530 

630 

740 

860 

900 

1,130 

20 

.ISO 

200 

270 

340 

420 

510 

600 

710 

820 

940 

1..070 

21 

.140 

190 

260 

320 

39Q 

480 

570 

670 

780 

890 

1,020 

22  , 

.140 

190 

240 

810 

880 

460 

640 

640 

740 

850 

970 

23  , 

.130 

180 

230 

290 

860 

440 

520 

610 

710 

810 

920 

24 

.130 

170 

220 

280 

350 

420 

500 

590 

680 

780 

890 

25 

.120 

160 

210 

270 

830 

410 

480 

660 

660 

750 

860 

26 

.110 

160 

210 

260 

320 

390 

460 

640 

630 

720 

820 

27 

.110 

1-50  • 

200 

250 

310 

870 

440 

520 

610 

690 

790 

28 

.110 

140 

190 

240 

800 

860 

430 

600 

680 

670 

760 

29 

.110 

140 

180 

230. 

290 

850 

410 

490 

660 

640 

740 

To  obtain  the  safe  load  for  any  thickness:    Multiply  values 
for  1  inch  by  thickness  of  beam. 

To  obtain  the  required  thickness  for  any  load:    Divide  by 


safe  load  'for  1  inch. 


—Carnegie  Pocket  Book. 


Weight  of  Bolts. 


105 


TABLE    XVII. 

WEIGHT,  IN  POUNDS,  OF  100  BOLTS  WITH  SQUARE 
HEADS  AND  NUTS. 


.Length 

DIAM 

ETEB    01 

BQLTS- 

-INCRB 

8. 

Under  Head 

to  Point 

M 

A 

M 

& 

Mi 

M 

M 

H 

1 

18 

.   4.0 
.  4.4 

7.0 
7.5 

10.5 
11.3 

15.2 
16.3 

22.5 
23.8 

39.5 
41.6 

63.0 
66.0 

.... 

... 

j 

.  4.8 

8.0 

12.0 

17.4 

25.2 

43.8 

69.0 

109.6 

163 

58 

.   5.2 
.  5.6 

6.5 
9.0 

12.8 
13.6 

18.5 
19.6 

26.6 
27.8 

45.8 
48.0 

72.0 
75.0 

113.3 
117.5 

169 
174 

•M 

.  6.8 

9.6 

14.3 

20.7 

29.1 

50.1 

78.0 

121.8 

180 

8 

.  6.3 

10.0 

15.0 

21.8 

80.5 

52.3 

81.0 

126.0 

186 

||| 

.  7.0 

11.0 

ltt.5 

24.0 

33.1 

56.5 

87.0 

134.3 

196 

4 

.  7.8 

12.0 

18.0 

26.2 

35.8 

60.8 

93.1 

142.5 

207 

«H 

.  8.5. 

13.0 

19.5 

28.4 

38.4 

65.0 

99.1 

161.0 

818 

5 

9.3 

14.0 

21.0 

30.6 

41.1 

69.3 

lt)5.2 

169.6 

829 

||| 

.10.0 

15.0 

22.5 

32.8 

43.7 

78.5 

111.8 

168.0 

840 

o 

10.8 

16.0 

24.0 

35.0 

46.4 

77.8 

117.3 

176.6 

861 

•M 

25.5 

87.2 

49.0 

82.0 

123.4 

185.0 

868 

7 

27.0 

39.4 

61.7 

86.8 

129.4 

193.7 

873 

TM 

28.5 

41.6 

54.3 

90.5 

135.0 

202.0 

884 

8 

30.0 

43.8 

59.6 

94.8 

141.5 

210.7 

895 

| 

46.0 

64.9 

103.3 

153.6 

227.8 

817 

in 

48.2 

70.2 

nr.8 

165.7 

244.8 

839 

i"          * 
11 

... 

... 

60.4 

75.5 

120.3 

177.8 

261.9 

860 

IB 

52.6 

80.8 

128.8 

189.9 

278.9 

882 

18 

86.1 

137.8 

202.0 

296.0 

404 

49 

f  J 

91.4 

145.8 

214.1 

313.0 

426 

IS 

96.7 

154.3 

226.2 

330.1 

448 

10 

102.0 

162.8 

238.3 

847.1 

470 

*v 

n* 

107.3 

171.0 

250.4 

864.8 

498 

. 

112.6 

179.5 

262.6 

881.8 

614 

j 

117.9 

188.0 

274.7 

898.3 

686 

' 

80 

123.2 

206.5 

286.8 

416.8 

668 

Per  incfc 

1.4 

2.1 

S.I 

4.8 

6.5 

8.5 

12.8 

16.7 

81.8 

Additional. 

WEIGHT  OF  NUTS  AND  BOLT-HEADS  IN  POUNDS. 
For  Calculating  the  Weight  of  Longer  Bolts. 


Diam  of  Bolt  in  Inches. 

1A 

H 

1A 

H 

M 

H 

Weight  of  Hexagon  Nut 

.017 

057 

.128 

267 

.43 

73 

Weight   of    Square   Nut 
and  Head  

021 

069 

164 

320 

55 

88 

Diam  of  Bolt  in  Inches. 

1 

154 

1# 

1)4 

2 

2J* 

8 

Weight  of  Hexagon  Nut 
and  Head        .     .   . 

1  10 

2  14 

3  78 

6  6 

8  75 

17  0 

28  8 

Weight   of    Square   Nut 

1.31 

2.56 

4.42 

7.0 

10.5 

21.0 

36.4 

— Carnegi*    Poctet 


106  Reinforced  Concrete. 

At  one  end,  or  at  both  ends  of  all  walls,  there  should  be  a 
hole  in  the  form,  the  bottom  of  the  hole  being  level  with  the  top 
of  the  concrete  already  poured.  This  hole  is  to  enable  the  space 
between  forms  to  be  thoroughly  cleaned.  It  is  impossible  to  raise 
the  waste  matter  so  the  best  way  is  to  provide  a  hole  through 
which  to  drive  it.  In  the  bottom  of  all  column  forms  there  should 
be  a  hole.  In  the  bottom  of  all  beam  and  girder  forms  there 
should  be  a  generous  sized  hole.  These  holes  are  absolutely  neces- 
sary to  secure  a  good  job  and  no  great  ingenuity  is  required  to 
devise  efficient  methods  for  closing  them.  It  does  require  watch- 
fulness however  to  insure  their  being  closed  before  pouring  begins. 
For  this  reason  a  definite  location  for  all  such  holes  should  be 
determined  beforehand  and  adhered  to.  For  example,  in  columns 
the  holes  may  be  on  the  north  side  and  for  walls  in  the  middle 
of  the  space  between  cross  walls  and  for  beams  at  the  north  end 
and  at  the  west  end. 

Forms  must  be  so  attended  to  that  concrete  cannot  adhere 
to  them  and  thus  make  a  rough  looking  job.  Wooden  forms  oiled 
should  be  thoroughly  soaked  in  crude  oil  and  each  time  they  are 
used  they  should  be  again  coated.  The  objections  to  oil  are  the 
expense,  the  weight  of  oil-soaked  forms  in  handling,  the  liability 
of  making  the  wall  dirty,  and  the  fact  that  if  the  walls  require 
plastering  or  any  subsequent  treatment  the  oil  skin  must  first  be 
removed  at  great  expense. 

Soap  is  excellent.  It  should  be  dissolved  in  water  to  the 
consistency  of  very  thin  paste  and  is  applied  with  brushes.  The 
objections  are  that  it  is  expensive  and  is  seldom  applied  properly. 
The  use  of  soap  helps  make  a  dense  surface  and  does  not  inter- 
fere materially  with  subsequent  treatment,  provided  the  surface  of 
the  concrete  is  washed  well  with  clean  water  before  applying  the 
treatment  or  plaster. 

The  cheapest  and  most  satisfactory  all  round  method  for 
securing  a  good  surface  is  to  thoroughly  soak  the  forms  with 
water  so  they  will  not  absorb  water  from  the  concrete.  A  sprinkling 
of  the  inside  with  a  hose  is  not  sufficient.  See  that  the  hose  is 
applied  to  both  sides  thoroughly  until  the  boards  can  take  up  no 
more  water.  When  dry  spots  appear,  wet  them. 

The  surface  obtained  with  oiled,  soaped  or  wetted  forms  is 
practically  identical.  The  great  objection  to  water  is  that  it  is  not 
always  possible  to  thoroughly  wet  the  forms  and  many  times  it 
is  absolutely  impossible  to  keep  them  wet  without  adding  too 
much  water  to  the  concrete  already  poured.  Hot  summer  days, 


Treatment  of  Surface.  107 

for  example,  are  poor  days  in  which  to  use  wetted  boards  unless 
there  is  a  plentiful  supply  of  water  and  it  can  be  applied  from 
the  outside. 

The  following  rules  deserve  to  be  printed  in  large  type  and 
pasted  in  the  hats  of  all  foremen  or  in  places  where  all  the  men 
can  read  them: 

See  that  all  the  steel  goes  in.     Check  closely. 

See  that  all  the  steel  is  wired  in  position. 

See  that  forms  are  well  scraped  and  cleaned  and  properly 
"doped"  before  concrete  is  poured. 

See  that  forms  are  in  line  and  are  plumb. 

See  that  the  proper  space  between  forms  is  obtained. 

See  that  all  bracing  or  wiring  is  done. 

See  that  all  holes  are  closed  and  all  cracks  stopped  up  with 
soft  clay  well  tamped  into  the  spaces. 

All  joints  should  stop  with  a  key.  Never  allow  sloping 
joints.  Vertical  joints  should  be  vertical  and  consist  of  a  board 
placed  across  the  form  having  on  the  side  towards  the  con- 
crete a  key  equal  in  width  to  one-half  the  thickness  of  the  wall 
and  projecting  into  the  concrete  a  depth  equal  to  at  least  one 
and  one-half  times  the  thickness  of  the  key.  It  should  be  so 
shaped  that  it  will  admit  of  comparatively  easy  removal.  This 
will  make  a  groove  in  the  end  of  the  wall  which  will  assist  ma- 
terially in  bonding  the  new  work  to  the  old.  A  similar  groove 
should  be  made  in  the  top  of  all  concrete  when  pouring  is  stopped 
and  in  this  groove  should  be  poured  a  water-tight  compound  of 
some  sort  if  the  walls  are  to  be  water  tight,  for  it  is  at  the  joints 
most  leaks  occur. 

In  joining  new  work  to  old  (meaning  to  concrete  poured 
so  long  that  it  has  alreday  set),  see  that  the  old  surface  is 
scrubbed  vigorously  with  a  wire  brush.  The  excess  of  water 
rising  to  the  surface  as  concrete  sets  contains  a  great  deal  of 
partially  set  cement.  It  forms  a  muddy  deposit  on  top  and 
slowly  sets  and  forms  a  scale  hard  to  detach  yet  which  pre- 
vents a  perfect  bond.  It  must  be  gotten  rid  of  at  any  cost. 
Brushing  with  wire  brushes  is  one  method.  A  solution  of  ten 
per  cent  chemically  pure  hydrochloric  acid  in  ninety  parts  of 
water  has  been  used  for  years  for  plain  concrete  work.  Its  use 
in  reinforced  work  is  questionable  on  account  of  the  acid  having 
a  tendency  to  go  down  the  very  small  space  between  the  steel 
and  concrete,  ultimately  destroying  the  adhesion.  When  acid 
is  used  it  must  be  washed  off  with  clear  water. 


108  Reinforced  Concrete. 

Compressed  air  has  been  used  to  clean  shavings  and  sawdust 
out  of  forms  with  great  success.  The  writer  used  on  a  piece  of 
work  he  had  charge  of  the  past  winter  (1907-8)  live  steam  at  a 
pressure  of  considerably  over  one  hundred  pounds.  He  was  so 
well  pleased  with  results  that  hereafter  the  use  of  steam  will  be 
required  in  his  specifications. 

Nothing  is  so  absolutely  bad  for  joints  as  sawdust  and 
nothing  is  so  hard  to  get  rid  of.  Shavings  and  blocks  of  wood 
are  picked  up  with  rag  pickers'  sticks,  which  are  pieces  of  wood 
about  one  inch  square  having  a  sharpened  nail  driven  into  one 
end.  Loose  gravel,  etc.,  can  often  be  brushed  out.  Sawdust 
however  remains.  Even  a  strong  stream  of  water  fails  to  get 
rid  of  it.  Live  steam  at  a  high  pressure  will  however  clean  off 
the  surface  of  the  concrete  to  the  bone.  It  removes  all  the  half 
set  and  dead  cement  and  all  the  sawdust.  The  writer  also  used 
this  steam  to  clean  his  forms.  It  was  directed  against  the  forms 
until  the  concrete  adhering  to  them  softened,  when  it  was 
scraped  off  readily. 

Knock  all  loose  scale  from  the  steel  before  cleaning  the  space 
for  another  pouring.  Clear  the  steel  entirely  of  all  concrete 
that  may  have  become  attached  during  the  previous  pouring. 
This  is  imperative.  When  this  cleaning  is  done  remove  all  the 
dirt  and  dust  before  erecting  the  next  set  of  forms.  After  the 
next  set  is  erected  clean  out  the  space  with  the  rag  pickers'  rods 
and  then  with  steam. 

Before  pouring  see  that  the  surface  of  the  old  concrete  is 
thoroughly  wet.  Then  give  it  a  coat  of  neat  cement  applied 
preferably  with  a  brush.  After  the  neat  cement  wash  has  been 
applied,  deposit  an  inch  of  cement  mortar  pretty  wet,  composed 
of  one  part  of  cement  and  two  parts  of  sand.  This  should  not  be 
poured  but  should  be  thrown  in  with  shovels,  half  a  shovelful 
at  a  time.  Then  begin  to  deposit  the  concrete.  If  the  joint  is 
vertical  and  the  mortar  cannot  be  readily  applied,  use  rods  or 
spades  or  pieces  of  wood  to  work  the  mortar  in  the  concrete  up  to 
the  face  of  the  joint  and  into  the  key.  It  is  imperative  that  old 
concrete  be  well  soaked  with  water  before  new  concrete  is  joined 
to  it. 

Experiments  lately  made  in  France  showed  that  practically 
perfect  joints  were  made  by  first  thoroughly  wetting  the  old 
surface  and  then  painting  it  with  neat  cement  paste  and  thor- 
oughly tamping  a  layer  of  concrete  on  top  before  proceeding 
to  fill  the  forms.  This  tamping  was  good  hard  pounding,  and 


Making  of  Joints.  109 

this  is  a  good  thing  to  know,  for  joints  are  hard  to  make.  Up 
to  the  present  time  perfectly  satisfactory  joints  between  old 
and  new  work  were  deemed  to  be  a  practical  impossibility.  The 
reinforcement  may  be  in  the  way  of  getting  the  hard  pounding 
in  thin  walls,  but  still  some  of  the  pounding  may  be  secured. 

When  possible  to  precure  the  men,  work  should  be  carried  on 
in  two  eight  hour  shifts  for  the  concreting  gang  and  three  eight 
hour  shifts  for  the  form  gang  so  that  not  more  than  eight  hours 
will  intervene  between  pourings.  Sometimes  the  carpenters 
are  worked  on  the  two  eight  hour  shifts  having  daylight  and  the 
laborers  are  worked  on  three  shifts.  The  contractor  should  not 
be  permitted  to  evade  this  method  until  an  actual  trial  demon- 
strates the  impossibility  of  doing  it  and  getting  a  satisfactory  job. 

Work  left  over  night  must  have  the  surface  roughened  before 
the  concrete  is  entirely  set.  When  forms  are  removed  the  walls 
must  be  at  once  attended  to.  If  appearance  is  an  object  all  pro- 
jections must  be  removed  by  chiselling  or  bush  hammering.  All 
pitting  must  be  brushed  out  with  steel  brushes  until  the  surface 
is  rough.  It  must  then  be  soaked  with  clean  water,  painted  with 
a  neat  cement  wash  and  plastered  with  a  one  to  two  or  one  to 
three  mortar  floated  with  a  wooden  float  to  the  level  of  the 
surrounding  concrete.  The  finish  should  be  a  sand  floated  surface 
for  this  patching.  Do  not  point  up  with  a  mortar  richer  than 
the  mortar  used  in  the  matrix  of  the  concrete,  for  cracks  will 
appear  around  the  edges  of  the  patch,  besides  which  the  color 
will  be  different. 

If  the  appearance  of  the  work  requires  a  coat  of  plaster,  clean 
the  surface  with  steam,  afterward  using  wire  brushes  and  then  the 
steam  again.  Wet  it  with  water,  paint  it  with  neat  cement  and 
immediately  follow  with  two  coats  of  one  to  three  mortar,  the 
lower  coat  scratched  and  the  top  coat  wood  floated  to  a  sand 
surface. 

For  work  done  in  cold  weather  the  writer  uses  steam  and  hot 
water.  He  has  steam  pipes  perforated  with  small  holes  running 
all  through  the  sand  pile  and  the  steam  continually  escaping.  It 
is  well  to  have  this  done  under  the  stone  pile  as  well,  using  only 
the  stone  that  has  no  ice  on  it  and  the  sand  that  is  not  lumpy, 
for  the  lumps  may  be  frozen  sand.  He  has  a  steam  coil  in  a 
water  barrel  to  get  the  water  almost  to  boiling  heat  and  the 
steam  pipe  ends  in  the  mixer  drum,  keeping  it  so  hot  that  it  is 
warm  to  the  hand.  A  little  salt  added  to  the  water  also  is  used 
occasionally. 


110  Reinforced  Concrete. 

Sometimes  long  cylinders  of  sheet  steel  are  laid  on  their 
side  and  over  them  are  placed  coarse  screens.  A  fire  of  scrap 
form  lumber  is  kept  going  in  the  cylinders  and  a  stove  pipe  in 
the  farther  end  insures  a  draught.  The  sand  and  stone  are 
shovelled  over  the  screens  and  lumps  thus  broken  up,  the 
materials  falling  down  to  the  hot  cylinder  and  keeping  warm 
until  used. 

Hot  concrete  sets  up  quickly.  If  it  obtains  its  initial  set 
inside  of  thirty  minutes  add  a  little  cold  water  while  mixing,  to 
reduce  the  temperature.  Heat  the  steel  and  inside  of  the  forms 
before  pouring  concrete.  This  is  done  best  with  steam,  followed 
by  hot  water.  It  is  a  mistaken  notion  that  hot  water  freezes  more 
quickly  than  cold  water. 

Some  European  experiments  seemed  to  show  that  hot  con- 
crete is  much  weaker  than  concrete  mixed  with  cold  water. 
Little  has  been  said  about  it  in  America,  but  the  general  cus- 
tom is  to  use  hot  water,  and  some  men  even  heat  the  stone, 
believing  that  it  will  hold  the  heat  a  long  time.  The  writer  does 
not  approve  of  this  heating  of  stone  and  sand,  but  merely  warms 
them  enough  to  take  the  frost  and  ice  out  of  the  voids.  The 
water  he  does  not  allow  to  reach  the  boiling  point,  and  if  the 
stones  are  not  hot  they  will  prevent  the  mixture  from  becoming 
warm  enough  to  injure  the  cement. 

Calcium  chloride  is  the  best  material  known  to  prevent  con- 
crete from  freezing  before  it  sets.  About  one  pound  per  bag 
of  cement  seems  to  be  sufficient  and  all  tests  made  seem  to  show 
that  the  strength  of  the  concrete  is  increased. 

If  possible  it  is  a  good  idea  to  have  a  salamander  in  the 
room  under  the  floor  that  is  being  poured  to  prevent  the  under 
side  of  the  forms  from  getting  too  cold.  Yet  there  is  danger 
of  the  concrete  baking  in  the  forms,  so  it  is  well  to  have  the 
under  side  continuously  sprinkled  with  cold  water  until  they  do  not 
feel  warm  to  the  hand. 

Salamanders  should  be  kept  burning  during  the  night  in  con- 
creted rooms  or  tanks  and  in  freezing  weather  all  surfaces  of 
concrete  poured  during  the  day  should  be  covered  with  sawdust 
or  straw.  Old  manure  is  heating  but  fresh  manure  is  injurious 
to  fresh  concrete.  Boards  placed  one  inch  above  the  surface  of 
floors  and  covered  with  sacks  or  straw  make  a  good  covering. 


CHAPTER  VIII. 
TOOLS. 


When  ordering  steel  for  a  piece  of  work  it  is  usual  to  have 
the  mills  cut  all  the  pieces  to  lengths,  especially  when  there  is  no 
extra  charge  for  such  cutting. 

It  is  almost  impossible  to  keep  exactly  to  the  schedule,  as  men 
will  make  mistakes,  especially  when  working  with  pieces  varying 
by  only  a  few  inches,  so  it  is  better  to  cut  some  of  the  steel  on 
the  job.  A  good  rule  to  follow  is  to  have  no  pieces  cut  to  lengths 
when  less  than  twenty-five  of  any  certain  length  are  required. 
When  less  than  that  number  may  be  wanted  then  order  long  pieces 
in  multiples  of  the  required  lengths,  exactly  as  a  carpenter  orders 
lumber. 

Every  job  should  have  a  shear  for  cutting  steel  into  lengths 
required.  Such  shears  cost  from  fifteen  to  one  hundred  and  fifty 
dollars.  If  properly  used  a  fifteen  dollar  shear  is  about  all  that  is 
required.  The  writer  has  used  on  his  work  the  Badger  and  the 
Edwards  but  knows  that  there  are  others  as  good,  though  those 
mentioned  gave  perfect  satisfection.  With  them  he  has  cut  high 
carbon  twisted  steel  three-quarters  of  an  inch  square.  As  a  rule 
high  carbon  steel  is  easier  to  cut  than  medium  steel.  In  using 
such  shears  the  steel  should  be  pushed  well  into  the  jaws  and  bear 
well  against  both,  before  the  power  is  applied.  If  the  jaws  have 
to  move  a  little  before  coming  in  contact  with  the  bar  there  is 
danger  of  the  shear  being  broken  when  the  men  throw  their 
weights  on  to  the  handle.  All  the  bolts  on  the  shear  should  be 
tightly  screwed  up  also.  When  the  jaws  are  tight  the  best  work 
is  done. 

An  extremely  useful  tool  on  a  reinforced  concrete  job  is  a 
combination  shear  arranged  for  cutting  round,  square  and  flat  bars 
and  also  for  punching  holes  in  flats  half  an  inch  thick.  Such  a 
combination  shear  and  punch  costs  between  forty  and  fifty  dollars. 

Ill 


112 


Reinforced  Concrete. 


The  two   following  cuts  illustrate  the  method  the  writer  has 
adopted  for  keeping  track  of  his  steel. 


FOP 


I" 


Zlo 


/Of 


V* 


linru 


/Q 


Dotes 


f 


'./ 

IQe^S 


STEEL 

of-    %  *  Bars .        L&tqJbs  ih  feef 


7 
fttti    U&tt 


(0 


3 

f  (H> 


13    f*<* 


w. 


no 


feef 

Used 


SD 
1*0 


ff&c^f 


fee* 


When  he  sends  his  order  to  the  dealer  he  rules  on  a  page  in 
a  book,  as  many  columns  as  there  are  lengths  ordered,  as  shown. 
On  a  vertical  line  he  places  the  sizes.  Then  from  his  order  sheet 
he  copies  the  number  of  pieces  in  each  column  in  lead  pencil, 
As  each  car  is  received  the  number  is  checked  off  and  when  all 
the  steel  has  come  he  writes  the  number  of  pieces  in  each  column 
in  red  ink.  About  five  per  cent  surplus  should  be  ordered  in 
half  inch  bars.  Extra  pieces  are  often  wanted. 

He  also  has  a  small  blank  book  ruled  for  keeping  track  of  each 


Forms  and  Systems.  113 

size  and  the  lengths.  This  is  the  Steel  Record.  When  the  steel  is 
received  the  proper  entries  are  made  in  the  column  headed  "Re- 
ceived" and  as  the  steel  is  used  the  number  of  pieces  is  entered  in 
the  "Used"  column.  It  is  thus  an  easy  matter  at  all  times  to  know 
exactly  how  many  pieces  of  a  certain  size  and  length  there  should 
be  on  hand. 

The   following  cut  shows  how  orders  for  steel  are  given  to 
the  steel  boss: 


One  man  has  charge  of  the  steel  yard.  To  him  all  orders  are 
given  for  steel  to  be  delivered  in  the  building.  He  has  charge  of 
the  steel  bending  gang  also.  In  the  book  where  the  steel  record  is 
kept  all  orders  for  bending  or  delivery  of  steel  are  entered.  The 
book  is  turned  upside  down  and  entries  made  in  what  was  the  back. 
The  writer  generally  uses  a  quadrille  ruled  book  so  front  and  back 
are  merely  relative  terms.  The  accompanying  illustration  is  a  copy 
of  one  page  in  this  book.  The  steel  boss  has  a  small  leather  bound 
book  that  he  can  carry  in  his  pocket.  When  an  order  is  given  it 
is  first  entered  fully  in  the  office  book  and  entered  in  the  "Used" 


114  Reinforced  Concrete. 

column  of  the  Steel  Record.  Then  the  bending  order  is  copied 
into  the  steel  boss's  book  in  full,  date  also.  He  bends  the  steel  and 
piles  it  in  a  convenient  place  until  wanted. 

When  there  is  plenty  of  room  the  most  convenient  way  to  take 
care  of  the  steel  is  to  put  it  in  piles  on  the  ground  with  posts  along- 
side telling  the  size  and  length.  If  there  is  not  much  room  then  a 
steel  rack  must  be  made.  These  racks  are  simple  and  do  not 
require  description.  Any  intelligent  carpenter  should  be  able  to 
make  one  after  inspecting  the  store  room  of  a  hardware  dealer  or 
of  a  blacksmith  shop.  But  whether  the  material  is  laid  on  the 
ground  or  put  on  racks  one  man  alone  should  have  charge  of  it 
and  if  this  is  not  done  there  will  be  trouble. 

Formerly  on  every  job  a  blacksmith  was  employed  and  all 
bending  of  steel  was  done  by  first  heating  it.  A  blacksmith  is  as 
hard  to  get  as  a  carpenter,  although  many  hundreds  of  men  may 
apply  for  the  job  and  call  themselves  blacksmiths.  The  result  is 
that  much  of  the  steel  is  burned  and  weakened.  It  is  best  to  bend 
all  of  it  cold  but  there  should  be  a  forge  on  the  job  for  occasionally 
heating  steel  and  also  for  sharpening  and  tempering  picks,  gads, 
chisels,  etc. 

Nearly  all  the  benders  sold  are  intended  for  bending  metal 
hot.  The  writer  uses  a  bender,  which,  so  far  as  he  knows,  was 
developed  by  Mr.  R.  S.  Hunt,  C.  E.,  of  Charleston,  W.  Va.  It 
consists  essentially  of  a  bar  about  one  and  one-quarter  inches 
diameter  and  three  feet  long.  On  one  end  is  fastened  a  pintle  at 
right  angles,  of  the  same  diameter  and  about  one  foot  long.  This 
pintle  goes  down  through  a  piece  of  ten  by  ten  timber  used  as  a 
bench,  the  hole  through  which  the  pintle  goes  being  lined  by  an 
iron  pipe.  About  two  inches  away  from  the  pintle  is  another  one 
about  two  inches  long.  This  rests  upon  a  steel  plate  on  top  of  the 
bench.  The  steel  to  be  bent  is  placed  in  the  two-inch  slot  between 
the  two  projections  and  men  turn  the  bender  round.  The  writer 
has  bent  high  carbon  steel  cold,  one  inch  square,  and  medium  steel 
one  and  one-quarter  inches  square,  cold,  with  such  a  bender. 
Sometimes  the  smaller  projection  has  an  anti-friction  roller  on  it. 

Sometimes  it  is  necessary  to  bend  a  small  piece  of  steel  with 
a  shoulder  almost  square  and  this  is  done  by  placing  a  steel  pin  in 
a  hole  in  the  plate  a  short  space  away  from  the  large  pintle. 

The  hot  bender  is  a  small  bender  that  can  be  attached  to  an 
anvil  (which  should  be  on  the  job),  for  bending  rods  that  have 
been  heated  or  for  bending  very  small  rods  and  bars  cold.  It  is 
remarkably  efficient.  It  consists  first  of  a  round  piece  of  iron  about 


B. 


115 


116  Reinforced  Concrete. 

five  inches  long  with  a  square  extension  of  about  the  same  length 
to  fit  into  the  hole  on  the  anvil.  A  piece  of  three-quarter  inch 
round  steel  about  four  feet  long  is  split  at  one  end  and  the  pieces 
formed  into  a  yoke  about  eight  inches  long.  The  ends  have  holes 
to  fit  over  the  upright  round  piece  sticking  up  from  the  anvil. 
Along  the  sides  of  the  yoke  are  holes  to  hold  pins  which  shorten 
the  space  according  to  the  size  of  the  rod  to  be  bent.  When  the 
heated  rod  is  passed  through  the  yoke  between  the  upright  standard 
and  the  pin  run  through  the  sides  of  the  yoke  the  blacksmith  turns 
the  bender  so  the  bar  is  bent  to  any  required  degree.  There  should 
be  a  cold  bender  and  a  hot  bender  on  every  job. 

Hand  benders  are  readily  made  by  bending  some  pieces  of  the 
reinforcing  steel  on  the  job.  Three-quarter  inch  bars  are  best, 
although  sometimes  something  heavier  is  needed.  The  bar  is  first 
bent  at  right  angles.  Then  the  short  end  is  bent  again  parallel 
with  the  main  piece  and  about  an  inch  and  a  half  away  from  it. 
Then  at  a  distance  of  an  inch  it  is  bent  again  toward  the  main 
piece  thus  forming  a  letter  U  at  right  angles  to  the  bar.  Small 
pipes  are  used  satisfactorily  as  hand  benders  in  many  cases  but 
there  is  nothing  really  as  satisfactory  as  a  twenty-one  inch  monkey 
wrench. 

Occasionally  rods  and  bars  have  to  be  cut  in  situations  where 
it  is  impossible  to  use  the  shear,  so  for  such  work  cold  chisels 
must  be  used  and  a  plentiful  supply  should  be  on  hand.  They  are 
made  of  tool  steel  properly  hardened  by  a  competent  metal  worker. 
The  edge  is  held  on  the  steel  and  a  hand  hammer  used  for  striking. 
Cold  cutters  have  longer  edges  than  cold  chisels  and  are  fastened 
to  a  handle  like  a  hammer.  By  means  of  this  handle  the  cold 
cutter  is  held  in  place  by  one  man  while  another  does  the  striking 
with  a  sledge  hammer.  Cold  chisels  and  cold  cutters  are  useful 
and  occasionally  necessary  but  they  are  very  expensive  tools  to  use. 
While  they  should  be  on  the  job  it  is  seldom  any  use  will  be  had 
for  them  if  the  shears  are  properly  handled.  As  the  edges  go  fast 
a  number  must  be  handy  when  needed. 

Bolt  cutters  are  scissors-like  tools  having  jaws  of  well  tempered 
steel  and  powerful  levers  in  the  jaws.  They  come  in  several  sizes 
and  as  they  are  intended  for  cutting  iron  should  not  be  used  for 
cutting  steel  bars  although  some  are  large  enough  to  cut  a  half 
inch  bolt  readily.  The  best  size  to  use  on  a  reinforced  concrete 
job  is  the  No.  0,  intended  for  cutting  a  quarter  inch  bolt.  Many 
uses  will  be  found  for  bolt  cutters  as  considerable  wire  is  used. 
There  should  be  two  or  three  on  an  ordinary  job. 


Handy  Tools.  117 

A  pair  of  tinners'  snips  are  very  handy  and  also  a  few  pieces 
of  sheet  iron  for  making  a  smooth  job  of  patching  a  hole  in 
forms. 

The  handiest  tool  for  cutting,  tying  and  bending  the  small  wire 
(No.  16  or  No.  18)  used  for  fastening  steel  is  a  ten-inch  black- 
smith's cutting  nipper.  It  is  better  than  a  flat  plier  for  bending 
the  wire  and  the  end  jaw  is  good  for  cutting  close  to  the  surface 
when  wires  project.  These  nippers  can  be  used  for  cutting  wires 
as  heavy  as  No.  10,  but  to  do  this  requires  a  twist  of  the  wrist  few 
ignorant  unskilled  laborers  can  acquire,  and  the  edges  of  the  cutting 
nippers  are  broken,  rendering  the  tool  useless  for  anything  but 
bending. 

Flat  pliers  do  well  for  bending  but  there  should  be  a  cutting 
edge.  Some  of  the  many  fence  tools  on  the  market  are  good. 
They  combine  pliers,  wire  cutters,  staple  pullers  and  hammers. 
They  are  really  very  efficient  but  for  the  fact  that  the  cutting  edges 
are  on  the  side,  whereas  an  end  cutter  is  most  convenient.  The 
edges  of  all  cutters  break  quickly  when  used  by  the  average 
laborer  as  they  will  twist  the  wrong  way  in  spite  of  all  instruction. 
The  furnishing  of  pliers  and  cutting  nippers  is  expensive.  It  is 
really  a  good  plan  to  have  a  few  men  do  all  wiring  and  make  them 
furnish  their  own  pliers,  etc. 

Every  job  should  have  at  least  two  crowbars.  The  writer 
generally  has  a  number  of  pieces  of  the  reinforcing  steel  sharpened 
on  the  end  with  chisel-like  edges.  Such  bars  can  be  used  as  pinch 
or  crowbars  and  as  slicing  or  cutting  bars  in  breaking  out  keys 
or  chipping  concrete. 

Some  small  bars  with  claws  on  the  end  for  removing  forms 
and  drawing  nails  are  useful.  They  can  all  be  used  for  reinforce- 
ment toward  the  end  of  the  job,  A  number  of  chisels  for  cutting 
concrete  and  a  number  of  steel  gads  are  also  needed. 

A  couple  of  4  or  6  pound  sledge  hammers  on  a  job  will  pay 
for  themselves  many  times  over.  A  couple  of  post  mauls  come  in 
handy  and  a  post  auger  is  a  very  convenient  and  sometimes  neces- 
sary tool. 

Forms  give  way  suddenly  and  occasionally  there  are  heavy  tools 
or  pieces  of  machinery  to  raise,  so  there  should  be  about  four 
bottle  or  house-raising  jacks  on  the  job.  It  is  well  to  have  also 
a  good  rope  about  two  hundred  feet  long,  one  inch  in  diameter, 
with  a  set  of  triple  blocks.  There  should  be  several  half  or  three- 
eighths  ropes  and  some  hooks,  which  can  be  made  from  pieces  of 
reinforcing  steel,  for  raising  forms  and  cleaning  up.  A  timber  saw 
(cross  cut)  and  one  or  two  twenty-six  inch  hand  saws,  a  couple 


118  Reinforced  Concrete. 

of  hammers,  two  hand  axes  and  a  couple  of  pole  axes  should  be 
included  in  the  outfit.  The  carpenters  furnish  their  own  tools  of 
course,  but  these  tools  are  for  the  use  of  men  on  odd  jobs  at  which 
a  carpenter  would  not  be  put.  Two  or  three  plumb  bobs,  a  square, 
good  level  and  several  hundred  feet  of  chalk  line  (not  forgetting 
balls  of  chalk)  and  some  marking  crayons  and  pencils  must  not  be 
forgotten.  For  marking  steel  for  cutting  and  bending,  soapstone 
crayon  used  by  machinists  is  best. 

When  power  is  obtainable,  a  circular  saw  for  cutting  and 
ripping  lumber  for  forms  is  a  good  investment.  A  great  deal  of 
sawing  must  be  done  on  every  job  and  a  circular  saw  will  soon  pay 
for  itself.  The  writer  knows  some  contractors  who  have  planers 
and  buy  all  their  lumber  in  the  rough,  thus  saving  one  dollar  and  a 
half  per  thousand  in  first  cost  and  also  being  sure  of  getting  the 
stuff  when  in  a  hurry.  Surfaced  lumber  sometimes  demands  a  day 
or  so  extra  time  to  furnish. 

Several  nail  pullers  are  a  necessity.  There  should  also  be  a 
good  grindstone  on  the  job.  A  boring  machine  is  needed  if  there 
will  be  many  holes  to  bore,  as  for  wires  and  bolts  through  forms. 
Boring  such  holes  with  brace  and  bit  is  slow,  expensive  work  and 
the  holes  are  not  always  exact. 

On  a  reinforced  concrete  job.  big  bills  for  work  at  machine 
shops  run  up  with  alarming  frequency.  For  this  reason  it  is  well 
to  have  the  forge  and  anvil  mentioned  and  in  addition  there  should 
be  a  bench  vice,  pipe  cutter,  stocks  and  dies  for  threading  pipes 
and  taps  and  dies  for  bolts  and  rods.  These  articles  are  cheap  and 
oftentimes  one  niece  of  work  will  pay  for  the  entire  outfit. 

Some  concrete  mixers  admit  of  loading  directly  into  wheel- 
barrows and  with  such  mixers  no  loading  box  is  required.  When 
the  work  has  reached  a  height  where  a  concrete  hoist  is  put  in 
operation  there  should  be  a  box  into  which  to  dump  the  concrete 
and  from  which  to  load  the  wheelbarrows  or  carts.  Boxes  and 
chutes  of  steel  for  this  purpose  are  made  by  a  number  of  firms 
and  it  pays  to  buv  them  when  over  five  hundred  yards  must  be 
handled.  However,  they  may  be  made  on  the  job,  the  box  of  wood 
and  the  gate  of  sheet  steel.  While  the  home  made  ones  work  all 
right,  when  they  work,  they  are  likely  to  break  and  as  every  man  of 
experience  knows,  breaks  generally  occur  when  the  work  can  be 
prosecuted  advantageously  and  the  repairs  are  just  completed  when 
the  weather  changes.  The  hope  of  saving  a  few  dollars  should  not 
influence  the  contractor  in  the  making  of  tools  unless  he  can  make 
them  as  well  as  those  he  can  buy. 


119 


120  Reinforced  Concrete. 

The  writer  has  several  times  used  wooden  boxes  for  hoisting 
concrete  with  a  horsepower  hoist.  It  is  very  efficient  and  lessens 
the  cost  of  handling  concrete  amazingly.  Yet  one  or  two  careless 
droos  may  make  such  a  box  much  more  expensive  than  a  steel  box, 
high  priced  though  the  latter  may  be.  The  horsepower  hoist  in 
small  towns,  however,  is  excellent.  The  cost  is  about  one-fourth 
or  one-sixth  the  cost  of  a  gasoline  or  steam  hoist  of  equal  capacity 
and  it  may  be  required  only  a  few  days. 

The  ideal  power  for  all  purposes  is  electricity.  One  motor 
cannot  be  used  on  all  jobs,  however.  When  a.  contractor  possesses 
an  alternating  current  motor  and  can  get  oflly  direct  current,  or 
vice  versa,  he  expresses  violent  opinions  regarding  electricity  as  a 
motive  power.  If  alternating  current  is  supplied  then  his  motor 
must  be  suitable  as  regards  voltage,  phase  and  cycle.  The  differ- 
ences found  in  power  plants  may  require  a  contractor  to  own  a 
number  of  motors  for  one  mixer  and  hoist  if  his  work  covers 
much  territory.  Assuming,  however,  that  his  motor  can  be  used 
he  has  only  to  keep  the  apparatus  well  protected  from  rain  and 
dust  and  not  neglect  proper  lubrication.  To  throw  the  switch  is 
simple  and  any  man  can  do  it  after  one  showing.  The  power  is 
always  there  when  wanted.  The  absence  of  dirt  and  grease  and  the 
saving  in  cost  of  skilled  attendance  count  on  the  right  side  of  the 
ledger. 

Gasoline  engines  come  next  in  convenience  to  electricity.  The 
power  is  there  when  wanted  and  it  is  no  trouble  to  start  and  stop. 
Like  electricity,  no  skilled  attendant  is  necessary.  Simply  an  intelli- 
gent careful  man  is  needed.  The  trouble,  however,  lies,  in  the 
engines  sold.  Contractors  seldom  obtain  good  gasoline  engines  for 
they  look  alike  and  the  lowest  priced  are  seldom  the  best. 

The  best  of  gasoline  engines  give  trouble  occasionally.  The 
secret  in  operating  gasoline  engines  lies  in  attending  properly  to 
the  lubrication  and  in  keeping  them  absolutely  clean.  That  is, 
provided  a  good  engine  is  purchased.  A  gasoline  engine  sold  at  a 
low  price  and  not  guaranteed  by  a  responsible  firm  is  a  delusion 
and  a  snare.  As  cost  is  not  the  proper  criterion,  a  man  buying  a 
gasoline  engine  should  employ  a  competent  mechanical  engineer 
to  buy  it  for  him  or  else  pay  a  good  price  for  a  guaranteed 
engine. 

With  electricity  or  with  internal  combustion  motors  the  power 
when  on  is  paid  for.  When  not  used  the  expense  ceases.  Steam 
engines,  however,  require  that  steam  be  kept  up  ready  for  use 


Concrete  Hoists. 


121 


when  wanted.     This  means  expense  for  fuel  and  also  the  wages 

of  a  high  priced  attendant.  The 
engineer  must  be  licensed  in  most 
states  and  is  generally  a  union 
man.  When  an  engineer  is  em- 
ployed he  does  not  want  to  do  any 
other  work,  even  on  a  small  job 
with  a  small  mixer.  If  the  mixer 
is  a  fairly  good  sized  one  he  wants 
a  helper  to  act  as  fireman.  There- 
fore steam  engines  are  not  very 
satisfactory  on  jobs  where  the 
concreting  is  not  continuous.  Con- 
ditions do  not  always  permit  of 
coal  or  other  fuel  being  stored  or 
handled  on  the  job. 

The  foregoing  remarks  on  mo- 
tive powers  apply  especially  to 
summer  work.  Cleaning  between 
forms,  especially  between  rein- 
forcing steel  set  in  the  forms,  is 
almost  impossible 
with  brooms,  and 
washing  with  water 
is  not  always  feasi- 
ble because  the  re- 
quired pressure  can 
not  be  had.  Com- 
pressed air  is  most 
excellent  and  when 
electricity  or  gaso- 
line or  oil  may  be 
used  for  power 
there  should  be  an 
air  compressor  ca- 
pable of  furnishing 
plenty  of  air  at  not 

FIG.  26-RANsoME  CONCRETE  HOIST.  leSS     than     eiSh*y 

pounds   pressure,   to 

blow  out  dust,   sawdust,   etc.,  and   clean  the   forms.     As  there 
is  a  thin  film  formed  on  top  of  all  concrete  which  prevents  a 


122  Reinforced  Concrete. 

good  bond,  the  compressed  air  apparatus  should  be  provided 
with  a  sand  blast  to  roughen  the  surface. 

The  writer  has  found  compressed  air  excellent.  He  has  found 
steam  better.  In  winter  steam  is  the  ideal  power  for  it  is  capable 
of  so  many  uses.  The  boiler  should  be  large  and  situated  at  a 
convenient  point,  which  is  seldom  one  close  to  the  mixer.  One 
pipe  can  lead  to  the  engine  on  the  mixer  and  a  smaller  pipe  can 
be  led  in  a  coil  through  a  barrel  of  mixing  water  and  end  in 
the  drum,  which  will  be  kept  full  of  live  steam.  Another  line  can 
be  led  to  coils  under  the  piles  of  sand  and  stone  and  a  line  can  be 
led  to  the  building,  to  which  a  steam  hose  may  be  attached  for 
blowing  out  the  forms  and  cutting  the  skin  off  the  top  of  the 
concrete.  The  pressure  should  be  not  less  than  one  hundred  pounds. 
When  the  number  of  uses  to  which  steam  can  be  put  are  considered 
it  may  be  termed  the  ideal  thing  to  use  in  cold  weather  while 
electricity  and  gasoline  or  oil  are  better  in  warm  weather. 

The  loss  by  condensation  of  steam  is  great  in  long  pipes,  no 
matter  how  well  covered.  They  should  be  covered  and  if  the  con- 
densation is  considerable  some  simple  form  of  separator  should  be 
used  close  to  the  engine,  or  cylinders  will  be  damaged.  There  are 
a  number  of  excellent  coverings  in  the  market,  but  generally  ex- 
pensive. The  writer  reduced  condensation  once  about  fifty  per  cent 
by  enclosing  a  long  pipe  in  a  box  six  inches  square  with  a  cover 
that  would  shed  water.  Around  the  pipe  was  wrapped  two  thick- 
nesses of  asbestos  paper  and  the  box  was  filled  with  plasterers  hair, 
so  the  pipe  had  no  less  than  an  inch  of  this  hair  surrounding  it. 
Another  good  covering  is  composed  of  flour  paste  and  sawdust. 
This  is  placed  in  a  box  surrounding  the  pipe,  the  heat  from  which 
bakes  the  paste,  forming  the  air  spaces  so  necessary  for  insulation. 

Wheelbarrows  of  course  are  the  usual  conveyances  for  the 
delivery  of  concrete.  They  may  continue  to  be  so  for  delivery  of 
material  to  the  mixer,  but  many  forms  of  cars  and  buckets  are  often 
superior  for  delivery  of  concrete. 

The  size  of  wheelbarrows  has  already  been  mentioned.  The 
most  convenient  and  least  wasteful  wheelbarrows  made  for  con- 
crete work  have  the  bed  raised  two  or  three  inches  in  front.  This 
increases  the  capacity  and  prevents  slopping.  Such  wheelbarrows 
are  a  regular  article  of  manufacture  and  can  be  purchased  almost 
everywhere.  The  No.  2  size  is  probably  best  as  it  is  light  and  lasts, 
in  proportion  to  price,  as  well  as  any  made.  If  the  local  store 
does  not  handle  them  the  ordinary  pressed  bowl  barrow  mounted 
on  a  wooden  frame  can  be  readily  altered  by  cutting  down  the 


FIG.  27 — SMITH'S  CONCRETE  HOIST. 

123 


Reinforced  Concrete. 


FIG. 


supports  for  the  bowl  near  the  handle  and  putting  bevelled  pieces 
under  the  bowl  near  the  wheel.  Some  men  favor  ball  bearing 
wheelbarrows  and  others  claim  the  old  fashioned  stapeled  squeaker 
to  be  better  than  the  ball  bearings,  for  the  latter  require  too  much 
oil.  The  writer  used  both  on  jobs  lately  completed  and  was  not 
able  to  decide  which  was  the  better.  He  uses  the 
ordinary  light  pressed  steel  bowl  barrow  for  carrying  sand  and 
stone  to  the  mixer  and  the  raised  bowl  concrete  wheelbarrow  for 
concrete,  there  being  a  difference  of  about  five  dollars  per  dozen 
in  the  price.  Of  one  thing,  however,  he  is  certain,  and  it  is  that  gas 
pipe  handles  on  wheelbarrows  are  not  favored  by  the  laborers.  It 
is  hard  to  get  a  wheelbarrow  crew,  with  such  handles  on  the 
work.  Some  contractors  have  enlarged  the  handles  by  putting 
rubber  hose  over  them  or  by  wrapping  them  with  cloth  and  sewing 
painted  canvas  over  the  wrappings.  The  pipe  handles  without 
some  covering  are  hard  to  hold  on  account  of  their  size  and  shape. 

When  running  plank  and  scaf- 
folds can  be  arranged  properly  two- 
wheeled  carts,  each  holding  six 
cubic  feet  of  wet  concrete,  are 
cheaper  and  better  to  use  than 
wheelbarrows.  Time  is  saved  in 
loading  from  the  mixer  and  in 
dumping  the  concrete  into  place. 
Two-thirds  of  the  wheelers  are 
also  saved.  One  cart  holds  as 
much  as  three  wheelbarrows,  but 
costs  as  much  as  six.  There  the 
difference  stops  and  is  all  the  other 
way  in  actual  use,  provided  the  car- 
rying is  all  done  on  a  level.  The 
only  objection  to  the  carts  is  that 
they  cannot  be  handled  well  on 
an  incline.  When  using  them  it 
is  best  to  use  a  hoist  and  take  the 
material  to  each  floor  level  so  there 
will  be  no  incline  up  which  to  push. 
Much  use  is  today  being  made 
of  derricks  with  bottom  dumping 
buckets,  thus  eliminating  wheelbar- 
rows and  carts.  When  the  job  is 
large  enough  to  warrant  the  cost  of 


28 — WALLACE-LI NDSMITH    HOIST. 


Conveyors.  125 

installation  some  such  method  should  always  be  used.  It  can  be 
used  to  carry  stone  and  sand  and  cement  from  stock  piles  to  the 
mixer  and  to  carry  the  mixed  concrete  from  the  mixer  to  the  forms. 
The  writer  wishes,  however,  to  go  on  record  as  being  opposed  to 
the  use  of  bottom  dumping  buckets  for  reinforced  concrete  walls 
less  than  eighteen  inches  thick. 

Another  method  is  to  have  cable  ways  from  the  mixer,  and 
one  system  contemplates  the  use  of  cable  ways  arranged  on  the 
cash  carrier  system  over  all  the  walls,  so  the  concrete  can  be 
delivered  at  any  point.  It  also  involves  a  similar  arrangement  for 
stone,  sand  and  cement  to  the  mixer. 

Another  system  provides  belt  conveyors  running  alongside  the 
walls,  with  adjustable  scrapers  to  throw  the  concrete  off  to  one 
side  and  into  the  forms.  There  is  also  a  system  consisting  of 
semi-circular  troughs  having  the  bottom  made  in  detachable  sec- 
tions a  couple  or  three  feet  long.  The  trough  contains  screw  con- 
veyors supplied  with  universal  joints.  The  bottom  is  one  sectfon 
shorter  than  the  frame  and  can  be  shifted  to  leave  a  hole  through 
which  concrete  will  drop  when  carried  to  the  point  by  the 
conveyor. 

Before  starting  a  piece  of  work  the  man  in  charge  should 
obtain  all  the  literature  he  can  on  the  subject  of  conveying 
machinery  for  contractor's  use.  Some  men  have  too  much 
machinery  and  some  do  not  have  enough.  It  pays  to  be  well 
equipped,  but  it  does  not  do  to  go  to  too  great  an  expense  for 
one  job.  If  a  man,  however,  does  not  wish  to  spend  enough 
money  to  prosecute  the  work  properly,  he  should  sublet  it 
rather  than  try  to  do  it  himself. 


INDEX 


Adhesion 10,  66 

formula    24 

length  of  steel  to   secure...   32 

Air,  compressed 108 

Amount  of  water 96 

Angle  steel  in  columns 50 

Areas  and  weights  of  steel 27 

Arm,  moment,  denned 15 

Axes    118 

Axis,    neutral,   denned 10 

formula    13 

tables   14-15 

Bag  and  barrel  of  cement 93 

Bars,  areas  and  weights 27 

bending  of 26 

deformed   18,  27,  67 

lap   26 

length   for   adhesion 10 

patented   17 

spacing  in  beams 10 

Base  of  walls 55 

Beams,    continuous 34 

design    of 14,  42 

double    reinforced 28 

failures   of 21,  24 

forms  for 91 

formulas 9 

loads   on 36,  43 

proportions    of 9,  10,  15 

spacing  of  bars  in 10 

of  T  section 30 

table  of  wooden 104 

Benders   for  steel 114 

Bending    bars 26 

steel   113 

Blacksmith    114 

Board  by  board  forms 77 

Boards,   thickness   for   forms....  102 

Bolt  cutters 116 

holes  in  walls 81 

Bolts  in  forms 79 

table  of 101,  105 

Bond  formula 24 

Bottle  jacks 117 

Boxes  for  concrete 118 

for    measuring 95 

Braced  forms 78 

Braces  and  posts,  loads  on 102 

Breadth,   proportion 9 

of  beam 15 

Bridges 43 

Buckling  of  steel 80 

Built-up  columns 45 

Cableways  124 

Calcium   chloride 110 

Cantilever  beams 88 

Carbon,  high,  steel 13 

Carpenters    70,  77 

Carts 124 

Cast-iron,    strength    of 10 

Cement  measuring 93 

Chalk  line 118 

Cheap  labor 71 

Chicago   ordinance 14,  43 

Chimney  design 61 

Cinder  concrete,  strength  of. ...  20 


Circular    tanks 69 

Cleaning    forms 106 

Coated    steel 68 

Cold  chisels 116 

Cold   cutters 116 

Cold    weather 109 

Column,   various   materials 44 

beam  acting  as 9 

divisors    47 

forms    91 

formulas     48 

footings 51,  63 

stresses    45,  46 

Compressed  air 108,  122 

Compression,    concentrated 13 

failure    24 

formula    22 

illustrated   11 

steel    30 

Compressive  strength  of  concrete  11 

Concrete,  below  steel 9 

columns    44 

joints    107 

protected   columns^ 45 

protection     10 

quantities  94 

stress  22 

walls   52 

weight  of 21 

Concentrated  loads 36,  43 

Condensation   of   steam 122 

Connections    32 

screwed    68 

Considered    tests 64 

Continuous  beams  and   slabs....   34 

Conveying  machinery 124 

Cast-iron  columns   44 

Cost  data 69 

estimates    73 

of    forms 75 

of   lumber 77 

of  placing  steel 28 

of  steel 18 

of  walls 68 

Counterforts    67 

Cracks  in  beams 64 

Crayon 118 

Crowbars    117 

Cutters,  for  steel Ill,  116 

Cutting  steel Ill 

Data  on  costs 70 

Dead  load 43 

on  columns 45 

Deflection,  defined 35 

of  beams 21,  65 

Deformation,  unit 12 

Deformed  bars 18,  67 

when  to  use 27 

Dense  concrete 97 

Design  of  beams 14 

Designing  forms 89 

Depth  of  beam,  definition 9 

proportions  9 

Depth  of  beam 16 

Diagonal  tension  failure 24 

defined   86 


126 


127 


Index. 


Distributed    loads 86,  43 

Distribution    of    steel 34 

Divisors,  for  column  design 47 

Double    reinforced   beams 28 

Drawing  of  wire 17 

Earth  pressure 53 

weight    of 56 

Elastic    limit 17 

Elasticity,  Modulus  of 13,  20 

Electricity    120 

Elevators   95 

Estimating  costs 73 

Expanded    fabric 27 

Fabrics  for  reinforcement 27 

Failures  of  beams 21 

of  walls  52 

Fence     tools 117 

Fibre    stress 17 

Finishing  work 109 

Finish  of  forms 92 

Jf  re    protection 10 

Floor  design 42 

loads   43 

slabs    83 

space,  value  of 44 

i  ootings  for  columns 51 

forms    for 90 

for  walls,  etc 63 

Forces  in  beams 12 

Forges  118 

Forms,  boards  for 102 

cost  of ». . . .   75 

designs   for 89 

per  cubic  yard 75 

Framed    forms 77 

Galvanized  steel 68 

Gasoline   engines 120 

Girder    forms 91 

Gravel,    pressure    of 53 

Greased   bolts 81 

Grip  of  concrete 10,  66 

Hammers   117 

Hand    mixing 94 

Heating  material 109 

Heaving   of   walls 56 

High  carbon  steel 13,  18 

Highway  bridges 43 

Hoists    95,  120 

Holders  for  planks 89 

Holes,  bolt,  in  walls 81 

in  forms 106 

in    slabs 68 

Hot  concrete 110 

Impervious  concrete 97 

Internal  stresses 15 

Iron,  cast,  strength  of 10 

columns    44 

Jacks,  house  raising 117 

Joints  in  concrete 107 

screwed    68 

K,  moment  factor 9 

Labor,  ideas  on 70 

Lap  of  bars 26,  68,  82 


Length  and  thickness  of  columns  45 

Limit,  elastic,  denned 17 

Line,    chalk 118 

Lining    forms 92 

Live  loads 43 

on  columns 45 

Loads,  allowed 43 

on   beams 36,  43 

on  columns 45 

dead  and  alive 43 

on  posts  and  braces 102 

on  supports 34 

Longitudinally      reinforced     col- 
umns    44 

Low  cost  labor 71 

Machine  mixing 94 

Manure    110 

Material  for  forms 77 

MeasuTing,    cement 93 

aggregates    95 

Medium  steel 13,  17 

Mixing  concrete 94 

Modulus  of  elasticity 13,  20,  65 

Moment,    defined 35 

arm  15 

factor    9 

formula    16 

table    16 

of  resistance 9 

formula    22 

Mortar  around  steel 99 

Nailing  forms 78 

Nail  pullers 117,  118 

Nails  and  spikes 108 

Neutral  axis 10 

formula    13 

table 14,  15 

Night  work 109 

Oiled    forms 106 

Ordering   steel Ill 

Ordinances,  Chicago 14 

St.   Louis 43 

fixing  stresses 81 

governing  loads 43 

Painted  steel 68 

Panel  forms 83 

Parabolic  formulas 21 

Parallel  forces 40 

Patented  bars 17 

Percentage  of  steel 13,  14,  18 

in  columns 47 

Pinch  bars 117 

Pipe  cutters 118 

Placing  steel 28,  98 

Placing  ttecl 93 

Plank  holders 87 

Plastering  109 

Pliers  117 

Plumbing  forms 92 

Posts  and  braces,  loads  on 102 

Pouring  columns 61 

concrete  92,  97,  98 

Pressure,  circular  tanks 69 

of   concrete 100 

different  materials , .  53 

against  walls 68 


128 


Reinforced  Concrete. 


Proportions  for  concrete 94 

of  beams 9,  10 

of  walls 50 

Protection  against  fire 10 

of  steel 9,  10 

Protected  concrete  columns 45 

Quantities  of  aggregates 94 

Racks  for  steel 114 

Ratio  of  modulus  of  elasticity..  21 

stress  29 

Reaction  defined 35 

Record  of  steel Ill 

Reinforcement,  double 28 

over  supports 32 

Resisting  moment 9 

Restrained  walls 58 

Retaining  walls 52 

Rock  concrete,  strength 20 

Rods,  areas  and  weights 27 

deformed  67 

Roof  slabs 33 

Round  rods 67 

Rules  for  foremen 107 

Rust  108 

St.    Louis   Ordinance 43 

Safety,   factor  of 19,  65 

Salamanders    110 

Sand  pressures 63 

Saw  dust 110 

Saws  118 

Scale   on   steel 108 

Screwed   connections 68,  32 

Shear 24,  25,  36,  43 

Shears  for  steel Ill 

Shrinkage,    in    columns 5! 

of   concrete 66 

Slabs,    continuous 34 

designing    83,  42 

Sidewalks    JJ 

Snips,  tinners 11 

Soap    1°6 

Spacers  between  bars 32,  10,  67 

in   walls 81 

Span,    proportionate 9 

Spikes  and  nails 103 

Spirally  wound  columns 4i 

Square    bars 67 

Steam    108,  122 

Steel    columns 4* 

in  compression 80 

cost  of 18 

cost   of   placing 28 

distribution  in  slabs 34 

galvanized  or  coated 68 

high  carbon 13 

medium    13 

ordering HI 

percentage  of 14,  18,47 

place  in  columns 50 

protection     9,  10 

record     HI 

formula  for  stress 16,  22 

too  much 21 

in  walls 56 

area  and  weights 27 


use  of  high  carbon 18 


Stirrups,    use    and    rules 25 

Straight  line  formulas 21 

Straw    110 

Strength    added    to    columns    by 

steel    49 

of  concrete 11,  20 

ultimate,  of  steel 18 

Stress,    fibre 17 

Stresses  fixed  by  ordinance 81 

illustrated    11 

internal    16 

ratio    of 89 

shearing  25 

steel  and  concrete 22 

Studded  forms 87 

Supports,    reinforcement   over...   38 

loads  on 34 

Surcharged  walls 53 

T  beams 30,  98 

Tamping   concrete 97 

Tanks,    circular 59 

Temperature   42 

Tensile  strength  of  concrete 11 

Tension    failure 24 

formula    22 

illustrated    11 

Testing    beams 64 

i  hawing  materials 109 

Thickness  of  boards  for  forms..  102 
Thickness  and  length  of  columns  45 

Thickness   of   slabs 33 

Tinners'    snips 117 

Top    reinforcement 82 

Twisted  bars 18,  67 

Turneaure's    tests 64 

Ultimate     strength,     vs.     elastic 

limit    18 

Unit    deformation 12 

Variation    in    concrete 65 

Vertically  reinforced  columns...   44 
Vertical    shear 24 

Wall  footings 63 

formulas    55 

pressures   53 

proportions    56 

restrained    58 

retaining    52 

Water,  amount  of 96 

pressure  of 53 

Weight   of   earth 56 

concrete   2! 

and  areas  of  steel 27 

Welded  fabrics 27 

Wetted  forms 106 

Wheelbarrows    95,  122 

Width  of  beam 16 

Wire  drawing 17 

table    101 

woeking 117 

Wiring  forms 79 

around  columns 44 

Wooden  beam  table 104 

Working   concrete , 97 

Wound   Columns 45 

Woven   fabrics 27 


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